Appeal from an order of the Supreme Court, Monroe County (Ann Marie Taddeo, J.), entered May 29, 2014. The order, insofar as appealed from, denied those parts of defendant’s motion seeking to dismiss plaintiffs’ fourth and sixth causes of action.
It is hereby ordered that the order insofar as appealed from is unanimously reversed on the law without costs, the motion is granted in part and the fourth and sixth causes of action are dismissed.
Memorandum: Plaintiffs commenced this action against defendant, Allstate Indemnity Company (Allstate), after their claim for property damage to their home under a policy issued by Allstate was disclaimed and denied. After answering the *1307complaint, Allstate moved, pursuant to CPLR 3211 (a) (1) and (7), to dismiss the fourth, fifth and sixth causes of action as well as plaintiffs’ demands for punitive damages and attorneys’ fees. Plaintiffs withdrew their fifth cause of action, which alleged unfair claim practices in violation of Insurance Law § 2601, and opposed the remainder of Allstate’s motion.
In the order in appeal No. 1, Supreme Court, inter alia, denied Allstate’s motion with respect to the fourth and sixth causes of action and reserved decision on that part of Allstate’s motion with respect to plaintiffs’ demands for punitive damages and attorneys’ fees. In the order in appeal No. 2, the court granted that part of Allstate’s motion to dismiss plaintiffs’ demand for attorneys’ fees and, because plaintiffs had withdrawn their fifth cause of action, the court “denied as moot” that part of Allstate’s motion to dismiss plaintiffs’ demand for punitive damages. In appeal No. 1, Allstate contends that the court erred in denying those parts of its motion seeking to dismiss the fourth and sixth causes of action and, in appeal No. 2, Allstate contends that the court erred in denying as moot that part of its motion seeking dismissal of plaintiffs’ demand for punitive damages.
We agree with Allstate in appeal No. 1 that the court erred in denying those parts of its motion to dismiss the fourth and sixth causes of action for failure to state a cause of action (see CPLR 3211 [a] [7]). We recognize that this appeal comes to us on a motion to dismiss pursuant to CPLR 3211 (a) (7), and “[t]hus, we accept as true each and every allegation made by plaintiff[s] and limit our inquiry to the legal sufficiency of plaintiff[s’] claim[s]” (Silsdorf v Levine, 59 NY2d 8, 12 [1983], cert denied 464 US 831 [1983]). Our role is thus to “determine only whether the facts as alleged fit within any cognizable legal theory . . . and ‘the criterion is whether the proponent of the pleading has a cause of action, not whether he [or she] has stated one’ ” (Leon v Martinez, 84 NY2d 83, 87-88 [1994]). Nevertheless, “ ‘[w]hile it is axiomatic that a court must assume the truth of the complaint’s allegations, such an assumption must fail where there are conclusory allegations lacking factual support’ ” (Dominski v Frank Williams & Son, LLC, 46 AD3d 1443, 1444 [2007]). Indeed, “ ‘a cause of action cannot be predicated solely on mere conclusory statements . . . unsupported by factual allegations’ ” (Ben Soep Co. v Highgate Hall of Orange County, 71 AD2d 825, 825 [1979]).
To the extent that the fourth and sixth causes of action allege bad faith, we note that, “in order to establish a prima facie case of bad faith, the plaintiff must establish that the insurer’s *1308conduct constituted a ‘gross disregard’ of the insured’s interests” (Pavia v State Farm Mut. Auto. Ins. Co., 82 NY2d 445, 453 [1993], rearg denied 83 NY2d 779 [1994]). We conclude in appeal No. 1 that the fourth and sixth causes of action “should have been dismissed because they do not allege [any] conduct by [Allstate] constituting the requisite ‘gross disregard of the insured’s interests’ necessary to support such causes of action” (Cooper v New York Cent. Mut. Fire Ins. Co., 72 AD3d 1556, 1557 [2010]). Moreover, the “[a]negations that [Allstate] had no good faith basis for denying coverage are redundant to [plaintiffs’] cause [s] of action for breach of contract based on the denial of coverage, and do not give rise to an independent tort cause of action, regardless of the insertion of tort language into the pleading” (Royal Indem. Co. v Salomon Smith Barney, 308 AD2d 349, 350 [2003]; see Dinstber v Allstate Ins. Co., 110 AD3d 1410, 1411-1412 [2013]).
Inasmuch as plaintiffs also demanded punitive damages in the fourth cause of action, we likewise agree with Allstate in appeal No. 2 that the court erred in denying as moot that part of its motion to dismiss the demand for punitive damages after plaintiffs withdrew the fifth cause of action. “A demand or request for punitive damages is parasitic and possesses no viability absent its attachment to a substantive cause of action” (Rocanova v Equitable Life Assur. Socy. of U.S., 83 NY2d 603, 616 [1994]). Here, the complaint fails to set forth “the pleading elements required to state a claim for punitive damages” (New York Univ. v Continental Ins. Co., 87 NY2d 308, 316 [1995]); plaintiffs’ "conclusory allegation [s] as to [Allstate’s] motive for [its] refusal [to pay the claim are] an insufficient premise for a demand for punitive damages” (Aldrich v Aetna Life & Cas. Ins. Co., 140 AD2d 574, 574 [1988]).
We further agree with Allstate in appeal No. 1 that plaintiffs failed to state a cause of action for untimely disclaimer in the sixth cause of action. “Where, as here, the underlying claim does not arise out of an accident involving bodily injury or death, the notice of disclaimer provisions set forth in Insurance Law § 3420 (d) are inapplicable and, ‘[u]nder the common-law rule, delay in giving notice of disclaimer of coverage, even if unreasonable, will not estop the insurer to disclaim unless the insured has suffered prejudice from the delay’ ” (Vecchiarelli v Continental Ins. Co., 277 AD2d 992, 993 [2000]; see Legum v Allstate Ins. Co., 33 AD3d 670, 670 [2006]; Rodriguez v Metropolitan Life Ins. Co., 251 AD2d 208, 208 [1998]; see generally KeySpan Gas E. Corp. v Munich Reins. Am., Inc., 23 NY3d 583, 590 [2014]). Contrary to plaintiffs’ contention, their *1309conclusory allegation that they were “damaged and prejudiced” by the untimely disclaimer is insufficient to withstand this CPLR 3211 (a) (7) motion to dismiss (see Tierney v Capricorn Invs., 189 AD2d 629, 632 [1993], lv denied 81 NY2d 710 [1993]).
Present — Scudder, P.J., Smith, Carni, Lindley and DeJoseph, JJ.