Under the bylaws of Axtel S.A. de C.V. (“Axtel”), a Mexican corporation, disputes between and among the company and its shareholders are subject to arbitration. Disputes have arisen between LAIF X SPRL (“LAIF X”) and Telinor Telefonía (“Telinor”). LAIF X contends that Telinor violated the Axtel bylaws by entering into a subscription agreement that illegally diluted LAIF X’s ownership interest in Ax-tel. Although the parties are currently arbitrating this dispute, LAIF X claims Telinor has in effect “refused” to arbitrate by filing a lawsuit in Monterrey, Mexico, that seeks a ruling that LAIF X took its shares by an invalid assignment and therefore is not a shareholder of Axtel.
In the current litigation, LAIF X seeks: (i) a order compelling Telinor to arbitrate the parties’ entire dispute; and (ii) an anti-suit injunction barring Telinor from pursuing any related foreign actions. On March 16, 2004, the United States District Court for the Southern District of New York (Rakoff, /.) denied LAIF X’s requests.
Since Telinor is currently submitting to arbitration with LAIF X, the district court did not err in refusing to issue an order compelling Telinor to arbitrate, ie., to do what it was doing. Nor did the district court abuse its discretion in declining to grant the anti-suit injunction, because: (i) *197principles of comity counsel against the anti-suit injunction; (ii) the Southern District of New York has no appreciable interest in Telinor’s Mexican suit; and (iii) Telinor has not attempted to “sidestep” arbitration.
The judgment of the district court is affirmed.
BACKGROUND
LAIF X is a limited partnership organized under the laws of Belgium. Its affiliate, LAIF IV Ltd. (“LAIF IV”), is a corporation organized under the laws of Bermuda. LAIF IV held subscription rights to purchase Series C shares of Ax-tel, a Mexican telecommunications company. LAIF IV assigned those subscription rights to LAIF X. Early in 2003, as part of its participation in Axtel’s debt restructuring, LAIF X exercised the subscription rights, at an exercise price of approximately $10 million, and obtained what LAIF X contends was a majority of Axtel’s Series C shares.
According to LAIF X: Axtel’s controlling shareholder, Telinor, entered into a subscription agreement on or about March 19, 2003, with Blackstone Capital Partners and several affiliated entities (collectively, “Blackstone”), by which Telinor acquired a block of Axtel Series A shares on Blackstone’s behalf, which Blackstone (or Teli-nor, or both) then converted to Series C shares; as a result of these transactions, LAIF X was deprived of its controlling interest in Axtel’s Series C shares and cannot exercise the governance rights for which it bargained; and the slate of Series C directors elected on October 9, 2003 is therefore illegitimate.
Article 60 of Axtel’s bylaws provides that disputes among shareholders are to be resolved by negotiation followed by arbitration:
Arbitkation: In the event of any dispute, claim, controversy or difference (a “Dispute ”) among the shareholders or between the shareholders and the Corporation, arising under or in connection with any of their respective rights and obligations under these bylaws or with their interpretation: ... Good faith efforts shall be used to settle such Dispute [through discussion and other non-binding means within 60 days and if a solution is not reached] any shareholder may treat the same as an arbitrable Dispute ... in which case the Dispute shall be submitted to a final and binding arbitration under the rules of the American Arbitration Association’s Commercial Arbitration Rules ....
Article 60 further specifies that arbitra-tions are to be held in New York City, and are subject to the New York Convention on Recognition and Enforcement of Foreign Arbitral Awards (the “New York Convention”), reprinted at 9 U.S.C.A. § 201.
On October 8, 2003, LAIF X initiated the negotiation process described in Article 60 to contest the conversion of Blackstone’s Series A shares to Series C shares. On October 24, 2003, LAIF X petitioned for interim relief in the judicial district of Monterrey, Mexico, a step that LAIF X claims was necessary to preserve its right under Mexican law to challenge the October 9, 2003 election of directors. On December 23, 2003, the sixty-day period of negotiation having elapsed without agreement, LAIF X filed a demand for arbitration with the AAA, seeking, inter alia, a declaration that the transfer and conversion of Series A into Series C shares by Blackstone or Telinor was void as contrary to Axtel’s bylaws.
Before filing an answer to LAIF X’s arbitration demand, Telinor commenced suit in Monterrey, Mexico (on or about January 26, 2003) against LAIF IV, LAIF *198X, and Axtel, seeking: “(1) a declaration that LAIF IV did not and does not possess subscription rights to Axtel stock and could not have validly transferred such rights to any other entity”; and “(2) a declaration invalidating the transfer of subscription rights from LAIF IV to LAIF X.” Telinor answered LAIF X’s demand for arbitration on February 11, 2004. In that answer, Telinor requested that the AAA dismiss the arbitration for lack of an arbitrable dispute and, alternatively, stay proceedings pending the outcome of Teli-nor’s Mexican lawsuit.
On February 17, 2004, LAIF X petitioned the United States District Court for the Southern District of New York for: (i) an order compelling Telinor to arbitrate the issue of LAIF X’s title to the Series C shares as part of the arbitration proceedings initiated by LAIF X in December 2003; and (ii) an anti-suit injunction enjoining Telinor from further pursuit of any related lawsuits (including Telinor’s Mexican lawsuit). The district court declined to grant any relief.
DISCUSSION
On this appeal, LAIF X contends that the district court erred: (i) in refusing to compel Telinor to arbitrate its entire dispute with LAIF X exclusively before the AAA; and (ii) in declining to issue an anti-suit injunction that would bar Telinor from pursuing its litigation in Mexico. This Court reviews the denial of a petition to compel arbitration de novo. Jacobs v. USA Track & Field, 374 F.3d 85, 88 (2d Cir.2004). The denial of a motion for an anti-suit injunction is reviewed for abuse of discretion. See, e.g., Paramedics Electromedicina Comercial, Ltda. v. GE Med. Sys. Info. Techs., Inc., 369 F.3d 645, 651 (2d Cir.2004); China Trade and Dev. Corp. v. M.V. Choong Yong, 837 F.2d 33, 37 (2d Cir.1987).
A. The Motion to Compel Arbitration
LAIF X contends that Telinor’s filing of a suit in Mexico that challenges LAIF X’s status as an Axtel shareholder amounts to a “refusal” by Telinor to arbitrate that entitles LAIF X to an order compelling Telinor to arbitrate, pursuant to the Federal Arbitration Act (“FAA”), 9 U.S.C. § 4.
Telinor argues that because it was already participating in the arbitration, there is no justiciable controversy among the parties and therefore no subject matter jurisdiction. Our jurisdiction is, however, sufficient to determine whether or not Telinor’s actions constitute a refusal to arbitrate under the FAA.
“Under the FAA, the role of courts is limited to determining two issues: i) whether a valid agreement or obligation to arbitrate exists, and ii) whether one party to the agreement has failed, neglected or refused to arbitrate.” Jacobs, 374 F.3d at 88 (internal quotation marks omitted). A party has refused to arbitrate if it “commences litigation or is ordered to arbitrate th[e] dispute [by the relevant arbitral authority] and fails to do so.” Id. at 89 (quoting Downing v. Merrill Lynch, Pierce, Fenner & Smith, Inc., 725 F.2d 192, 195 (2d Cir.1984)) (emphasis omitted); see also PaineWebber Inc. v. Faragalli, 61 F.3d 1063, 1066 (3d Cir.1995) (an action to compel arbitration accrues “only when the respondent unequivocally refuses to arbitrate, either by failing to comply with an arbitration demand or by otherwise unambiguously manifesting an intention not to arbitrate the subject matter of the dispute”).
LAIF X points out that Telinor has incontestably “commence[d] litigation,” that the litigation could bear upon LAIF X’s standing to compel arbitration as an Axtel *199shareholder, that Telinor has sought a stay from the AAA pending the determination of that issue in Mexico, and that Telinor thus has in fact and in effect “refused” to arbitrate notwithstanding its simultaneous participation in the arbitration.
It is difficult to see, however, how an order to compel would operate on Telinor’s course of conduct. Telinor has answered the arbitral demand. Telinor’s challenge to the arbitrability of LAIF X’s claims before the AAA does not constitute a refusal to arbitrate. See Jacobs, 374 F.3d at 89 (“The fact that respondents raised before the AAA an objection to petitioner’s Demand for Arbitration ... does not constitute a ‘refusal to arbitrate’ on the part of ^respondents.”). If the AAA concludes that the issues raised in Telinor’s Mexican lawsuit are not arbitrable and need to be decided before arbitration continues, the AAA will issue a stay, in which event Telinor’s conduct will be in accord with the arbitral process. It may be another story if the AAA denies a stay or if Telinor ignores an arbitral order to suspend or discontinue the suit in Mexico; but that has not happened.
Nor does Telinor’s commencement of suit in Mexico constitute a refusal to arbitrate. Telinor’s litigation in Mexico of certain claims arguably within the scope of the Axtel arbitration clause suggests that Telinor would prefer not to arbitrate those issues. Without an attendant refusal to arbitrate, however, this preference does not matter. LAIF X complains that a Mexican court might determine whether LAIF X’s allegations are arbitrable before the AAA has an opportunity to rule on the issue. However, where foreign law governs an issue that bears on standing to arbitrate, the submission of that issue to the competent foreign court, without more, does not constitute a refusal to arbitrate. As an investor in a Mexican company, governed by Mexican law, LAIF X cannot claim to be disadvantaged by a Mexican court’s decision regarding LAIF X’s shareholder status under Mexican law.
B. The Anti-Suit Injunction
A federal court has the power to enjoin parties before it from pursuing a foreign action; “[b]ut principles of comity counsel that injunctions restraining foreign litigation be ‘used sparingly’ and ‘granted only with care and great restraint.’ ” Paramedics Electromedicina, 369 F.3d at 652 (quoting China Trade, 837 F.2d at 36). That is because an anti-suit injunction, though directed at the litigants, “ ‘effectively restricts the jurisdiction of the court of a foreign sovereign.’ ” Paramedics Electromedicina, 369 F.3d at 655 (quoting China Trade, 837 F.2d at 35).
“An anti-suit injunction against parallel litigation may be imposed only if: (A) the parties are the same in both matters, and (B) resolution of the case before the enjoining court is dispositive of the action to be enjoined.” Paramedics Electromedicina, 369 F.3d at 652. Where these threshold requirements are satisfied, “courts are directed to consider a number of additional factors, including whether the foreign action threatens the jurisdiction or the strong public policies of the enjoining forum.” Id. at 652 (citing China Trade, 837 F.2d at 35). A salient consideration in this case is that, given “[t]he federal policy favoring the liberal enforcement of arbitration clauses,” an anti-suit injunction may be proper where a party initiates foreign proceedings in “an attempt to sidestep arbitration.” Paramedics Electromedicina, 369 F.3d at 654.
As to the initial considerations: the parties here dispute whether the parties in the Mexican litigation are identical to the parties in the arbitration, and whether the relief LAIF X requests in the Southern *200District would dispose of the Mexican litigation. Regardless of these considerations, however, the district court did not abuse its discretion by declining to issue the anti-suit injunction, because: (i) principles of comity counsel against issuing the anti-suit injunction; (ii) the United States federal courts have no interest in enjoining Telinor’s Mexican lawsuit; and (iii) Teli-nor’s Mexican lawsuit is not directed at sidestepping arbitration.
“Principles of comity weigh heavily in the decision to impose a foreign anti-suit injunction.” Id. at 654-55. “The fact that the injunction operates only against the parties, and not directly against the foreign court, does not eliminate the need for due regard to principles of international comity, because such an order effectively restricts the jurisdiction of the court of a foreign sovereign.” China Trade, 837 F.2d at 35 (internal citation omitted). Comity militates strongly against an injunction here. LAIF X invested in a Mexican enterprise, governed by Mexican law. A question has arisen under Mexican law — whether LAIF X is an Axtel shareholder — and that question has been presented to a Mexican court. Mexico has a strong interest in determining who is a shareholder of a Mexican corporation and whether particular transactions were permissible under the bylaws of a Mexican corporation.
On the other hand, the legal relationship between a Belgian investor and a Mexican enterprise in no way implicates “the strong public policies of the enjoining forum,” Paramedics Electromedicina, 369 F.3d at 652, which is the Southern District of New York.
Finally, although Telinor seeks a ruling of Mexican law from a Mexican court, Teli-nor continues to participate in the AAA arbitration. True, Telinor has sought a stay of the arbitration, but it has made that application in the arbitral forum. It has thus submitted itself to the arbitral forum, exercised its right in that forum to assert a procedural defense, and invoked the discretion of the arbitral forum to stay proceedings in deference to the Mexican court on a point of Mexican law. The arbitral forum may exercise its discretion as requested. If not, LAIF X may (or may not) seek intervention by the AAA in aid of whatever course or order of proceedings it prefers. All of that is in the future. But as of now, it cannot be said that Telinor’s conduct is an evasion of the arbitral forum or an “attempt to sidestep arbitration.” Id. at 654.
Under these circumstances, the district court did not abuse its discretion in refusing to issue an anti-suit injunction.
CONCLUSION
For the forgoing reasons, we affirm the district court’s ruling in its entirety.