ORDER
Arthur Bell, a Michigan prisoner proceeding pro se, appeals the district court’s judgment denying his petition for a writ of habeas corpus filed pursuant to 28 U.S.C. § 2254. Bell has also filed numerous motions for miscellaneous relief.
I.
The facts of this case are fully reported in our previous decision in Bell v. Howes, 703 F.3d 848, 849-50 (6th Cir. 2012) (Bell I), and are only briefly recounted here. On September 22, 1988, Priscilla Matthews and William “Herk” Thompson were in a Detroit motel room when the motel room door was kicked open. Two men entered, abducted Thompson, and drove off with him in a car. Matthews testified that Mark “Silver” Sylvertooth and an individual named “Chill” or “Chilly Will” abducted Thompson from the motel room, and that Thompson was driven away by Sylver-tooth, Chill, and Bobby Mims. Matthews testified that she knew Chill only by the names Chill or Chilly Will, and that he was not the same person as Bell. Sylvertooth, on the other hand, testified that he and Bell abducted Thompson from the motel room, and that Thompson was driven away by Sylvertooth, Bell, Durone Jenkins (a/k/a Otto Hilliard), and Mims. Sylvertooth testified that Bell later shot Thompson as he sat in the ear. When officers arrived at the scene, the suspects had fled on foot, and Thompson was dead inside the car.
Jenkins was never prosecuted, but he inculpated himself to police as the driver of the car in which Thompson was killed. Jenkins’s police statement also corroborated Sylvertooth’s factual recounting, except *410that Jenkins described the fourth suspect as “Tone.” Bell’s trial counsel later explained that “[everybody else clarified that Tone is Bell.” Bell I, 703 F.3d at 851.
On June 19, 1989, Bell was convicted in a bench trial of first-degree premeditated murder, felony murder, kidnapping, and possessing a firearm while committing a felony. The trial court imposed an effective sentence of life imprisonment without parole. On appeal, Bell argued in part that trial counsel was ineffective for failing to interview two alibi witnesses and present them at trial. The Michigan Court of Appeals remanded the case for an evidentiary hearing, and the trial court found that counsel had performed adequately. The Michigan Court of Appeals affirmed, and the Michigan Supreme Court denied leave to appeal. People v. Bell, 442 Mich. 877, 500 N.W.2d 473 (1993) (table).
II.
In 2006, Bell filed a federal habeas petition, raising four grounds for relief: (1) trial counsel conspired with the prosecution to deprive Bell of his “right to present witnesses, alibi witnesses, etc.”; (2) the state knowingly used perjured testimony to secure Bell’s conviction; (3) the trial court conspired to deprive Bell of a fair and impartial hearing under People v. Ginther, 390 Mich. 436, 212 N.W.2d 922 (1973); and (4) appellate counsel was ineffective for participating in “the conspiracy.” In investigating Bell’s claims, appointed counsel obtained the Detroit Police Department’s homicide file, which contained what was believed to be material, relevant evidence that the prosecution had not disclosed, in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Specifically, Bell claimed that the prosecution failed to disclose two items of evidence pertaining to Willie King, an individual who went by the nickname “Chilly Will” and lived near the location at which Thompson was last seen: First, the record of King’s 1989 arrest on the suspicion that he was the Chilly Will involved in Thompson’s murder, and second, King’s post-arrest statement to police (“the King documents”). The district court stayed Bell’s habeas proceeding to allow him to exhaust his Brady claim in state court. The trial court denied Bell’s Brady claim on the merits, and both the Michigan Court of Appeals and the Michigan Supreme Court denied leave to appeal. People v. Bell, 485 Mich. 1101, 778 N.W.2d 225 (2010) (Mem.).
In 2010, the district court re-opened Bell’s habeas petition and allowed him to amend his petition to include his Brady claim. After conducting an evidentiary hearing, the district court determined that habeas relief was warranted on Bell’s Brady claim and his claim that trial counsel was ineffective for failing to present alibi witnesses (“the IATC/alibi claim”). The district court declined to rule on Bell’s remaining claims. In 2012, we reversed the district court’s judgment and remanded for further proceedings on Bell’s remaining claims, finding that the state court’s rejection of Bell’s Brady claim was reasonable and that Bell’s IATC/alibi claim was barred by the statute of limitations. Bell I, 703 F.3d at 852-56.
On remand, the' district court granted Bell’s motion to amend his petition to add a claim that trial counsel was ineffective for failing to present evidence of third-party culpability (“the IATC/third-party claim”). The district court clarified that, because Bell’s IATC/alibi claim and his Brady claim had been rejected by this court, and his third claim was mooted by the district court’s 2010 evidentiary hearing, the claims properly before the district court were Bell’s IATC/third-party claim, the portion of his first claim that did not involve counsel’s failure to present alibi *411witnesses, and his second and fourth claims. On January 23, 2014, the district court denied Bell’s petition for a writ of habeas corpus, finding that his IATC/ third-party claim was procedurally defaulted and that his remaining claims were barred by the statute of limitations. The district court granted a COA “as to each of the claims addressed in [its] opinion.”
On appeal, Bell argues that the district court erred in denying him habeas relief.
III.
In an appeal from a district court’s denial of a § 2254 petition, we review the district court’s legal conclusions de novo and its factual findings for clear error. Loza v. Mitchell, 766 F.3d 466, 473 (6th Cir. 2014); Dando v. Yukins, 461 F.3d 791, 796 (6th Cir. 2006). We review the district court’s dismissal of a petition as barred by the statute of limitations or for procedural default de novo. Souter v. Jones, 395 F.3d 577, 584 (6th Cir. 2005) (statute of limitations); Lott v. Coyle, 261 F.3d 594, 606 (6th Cir. 2001) (procedural default).
A.
As to the remaining claims presented in Bell’s original habeas petition, the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”) imposes a one-year statute of limitations on petitions filed under § 2254. See 28 U.S.C. § 2244(d). Section 2244(d) states, in relevant part:
(1) A 1-year period of limitation shall apply to an application for a writ of habeas corpus by a person in custody pursuant to the judgment of a State court. The limitation period shall run from the latest of-
(A) the date on which the judgment became final by the conclusion of direct review or the expiration of the time for seeking such review;
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(2) The time during which a properly filed application for State post-conviction or other collateral review with respect to the pertinent judgment or claim is pending shall not be counted toward any period of limitation under this subsection.
Id. Because Bell’s conviction became final before the AEDPA’s effective date, his statute of limitations began to run on April 24, 1996. See McClendon v. Sherman, 329 F.3d 490, 493 (6th Cir. 2003), The remaining claims presented in Bell’s original habeas petition were filed well after the limitations period expired in 1997. Accordingly, absent equitable tolling, these claims are untimely.
A prisoner is entitled to equitable tolling of the limitations period if he can show that he diligently pursued his rights and was prevented from timely filing his habe-as petition by an extraordinary circumstance. Holland v. Florida, 560 U.S. 631, 649, 130 S.Ct. 2549, 177 L.Ed.2d 130 (2010). Alternatively, a demonstration of actual innocence may serve as a gateway for review of an otherwise barred claim. McQuiggin v. Perkins, 569 U.S. 383, 133 S.Ct. 1924, 1928, 185 L.Ed.2d 1019 (2013).
Bell argues that he is entitled to equitable tolling based only on his demonstration of actual innocence. “[Ajctual innocence means factual innocence, not mere legal insufficiency,” Souter, 395 F.3d at 590 (quoting Bousley v. United States, 523 U.S. 614, 623, 118 S.Ct. 1604, 140 L.Ed.2d 828 (1998)). In order to demonstrate actual innocence, a petitioner must present “evidence of innocence so strong that a court cannot have confidence in the outcome of the trial unless the court is also satisfied that the trial was free of nonharmless constitutional error.” Schlup v. Delo, 513 U.S. 298, 316, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995). An actual-innocence showing must *412rely on “new reliable evidence — whether it be exculpatory scientific evidence, trustworthy eyewitness accounts, or critical physical evidence — that was not presented at trial.” Id. at 324, 115 S.Ct. 851. “[Habe-as corpus petitions that advance a substantial claim of actual innocence are extremely rare,” id. at 321, 115 S.Ct. 851, and the Supreme Court has “counseled ... that the actual innocence exception should ‘remain rare’ and ‘only be applied in the “extraordinary case,” ’ ” Souter, 395 F.3d at 590 (quoting Schlup, 513 U.S. at 321, 115 S.Ct. 851).
In Bell I, we held that the King documents were insufficient to establish Bell’s actual innocence. 703 F.3d at 855-56. “[W]hen a case has been remanded by an appellate court, the trial court is bound to ‘proceed in accordance with the mandate and law of the case as established by the appellate court.’ ” Goldberg v. Maloney, 692 F.3d 534, 538 (6th Cir. 2012) (quoting Hanover Ins. Co. v. Am. Eng’g Co., 105 F.3d 306, 312 (6th Cir. 1997)). Thus, the district court properly found that the King documents could not serve to equitably toll the limitations period.
During the pendency of this appeal, Bell developed a new argument in support of his actual innocence: He now argues that two witness statements within the Detroit Police Department’s homicide file establish that Jenkins killed Thompson, and thus establish Bell’s actual innocence. Bell first points to Matthews’s September 23, 1988 statement to police, in which Matthews described the suspects’ seating arrangement as follows: “Bob [Mims] was the front passenger. Herk [Thompson] was in the back seat driver[’]s side and Silver [Sylvertooth] was in the back seat with Herk. When Chill came back from the [motel] room Chill jumped in the car and drove off with Bob, Herk, Silver, and Chill.” Bell argues that, by implication, this statement establishes that Chill was the driver of the car. Bell further argues that, because Jenkins admitted to being the driver of the car, this statement establishes that Jenkins was Chilly Will.
Bell also points to a September 26,1988 statement to police by witness Marvin Dickens. In this statement, Dickens told police that Mims told Dickens that “[Mims], Auto, and another guy beat the man and put him in the trunk of a car.... Auto and the other guy killed him.” Bell argues that, when considered in conjunction with Matthews’s statement and the fact that Jenkins was a better match for the physical description of Chilly Will than Bell, Dickens’s statement establishes that Jenkins (a/k/a Otto or “Auto” Hilliard) and Sylvertooth killed Thompson.
Bell did not present his argument concerning Matthews and Dickens’s statements in the district court. “It is a well-established principle of appellate review that appellate courts do not address claims not properly presented below,” Chandler v. Jones, 813 F.2d 773, 777 (6th Cir. 1987), except “to ‘prevent manifest injustice and to promote procedural efficiency,’ ” United States v. Baker, 807 F.2d 1315, 1321 (6th Cir. 1986) (quoting United States v. Cheama, 783 F.2d 165, 168 (10th Cir. 1986)). Even overlooking Bell’s failure to raise this argument below, the witness statements predicating Bell’s new claim are only minimally persuasive evidence of his actual innocence.
Dickens’s statement is hearsay, and is thus presumptively unreliable. See Herrera v. Collins, 506 U.S. 390, 417, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993). And both Matthews and Dickens’s statements are entitled to little weight because they are unsworn. See Teahan v. Almager, 383 Fed.Appx. 615, 615 (9th Cir. 2010) (unsworn statements of purported alibi witnesses were insufficient to establish actual inno*413cence). Moreover, Bell asks us to infer too much from too little. It would be equally plausible to infer from Matthews and Dickens’s statements that, although Jenkins was Chilly Will, Bell was the “other guy” who killed Thompson. Accordingly,' the proffered evidence is not “so strong that a court cannot have confidence in the outcome of the trial.” Schlup, 513 U.S. at 316, 115 S.Ct. 851. Bell’s new actual-innocence claim therefore fails.
B.
As to Bell’s IATC/third-party claim, Bell procedurally defaulted this claim by failing to raise it in state court. See Williams v. Bagley, 380 F.3d 932, 969 (6th Cir. 2004). If a claim is procedurally defaulted, “federal habeas review of the claims is barred unless the prisoner can demonstrate cause for the. default and actual prejudice as a result of the alleged violation of federal law, or demonstrate that failure to consider the claims will result in a fundamental miscarriage of justice.” Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). A habeas petitioner carries the burden of demonstrating cause and prejudice to excuse his procedurally defaulted claims, Lucas v. O’Dea, 179 F.3d 412, 418 (6th Cir. 1999), and may establish cause in two ways.
First, a petitioner may “show that some objective factor external to the defense impeded counsel’s efforts to comply with the State’s procedural rule.” Murray v. Carrier, 477 U.S. 478, 488, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986). The Supreme Court has noted “that a showing that the factual or legal basis for a claim was not reasonably available to counsel ... would constitute cause under this standard.” Id. The factual basis for Bell’s IATC/third-party claim was within the Detroit Police Department homicide file that formed the basis for his return to state court. Bell fails to identify any “objective factor external to the defense,” id., that impeded post-conviction counsel from arguing — as an alternative to Bell’s Brady claim — that, if the King documents (or the Matthews and Dickens statements) were produced, trial counsel was ineffective for failing to introduce them.
Second, a showing of constitutionally ineffective assistance of counsel may, under two limited circumstances, establish cause to excuse a procedural default. Id. at 488-89. Under the first circumstance, the complete abandonment by counsel during state post-conviction proceedings without notice to the petitioner may establish cause to excuse default. Maples v. Thomas, 565 U.S. 266, 288-89, 132 S.Ct. 912, 181 L.Ed.2d 807 (2012). Bell cannot establish that he was completely abandoned by post-conviction counsel. Under the second circumstance, the ineffective assistance of post-conviction counsel may establish cause to excuse default of a petitioner’s claim of ineffective assistance of trial counsel where a state procedural law prohibits defendants from raising ineffective assistance of trial counsel claims on direct appeal. Martinez v. Ryan, 566 U.S. 1, 17, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012). Because Michigan defendants may bring ineffective-assistance claims on direct appeal, see Taylor v. McKee, 649 F.3d 446, 452 (6th Cir. 2011), Bell may not avail himself of this circumstance.
Finally, a procedural default may be excused upon a demonstration that failure to consider a claim will result in a fundamental miscarriage of justice, which includes a colorable showing of actual innocence. See Bousley, 523 U.S. at 623, 118 S.Ct. 1604. Because the evidence that Bell submits in support of his actual-innocence claim — i.e., the statements of Matthews and Dickens — is only minimally persuasive *414evidence of his innocence, Bell has not demonstrated that failure to consider his IATC/third-party claim will result in a fundamental miscarriage of justice.
For these reasons, we AFFIRM the district court’s judgment and DENY Bell’s pending motions as moot.