This appeal requires us to address, for the first time, the question of whether the Federal Arbitration Act, 9 U.S.C. §§ 1-16 (1994) (the FAA), in and of itself confers subject matter jurisdiction on a federal court. We answer this question in the negative.

At all times material hereto, plaintiff-ap-pellee Unicom Corporation, a Puerto Rico entity, functioned as the general partner of plaintiff-appelle'e PCS 2000 LP (PCS), a limited partnership engaged in the business of acquiring so-called personal communications services licenses. PCS periodically participated in license auctions conducted by the Federal Communications Commission (the FCC). To assist in this endeavor, PCS enlisted the services of defendant-appellant Romulus Telecommunications, Inc. (Romulus), a Puerto Jlico corporation, as its bidding agent. The Service Agreement between PCS and Romulus contained an arbitration clause providing that “[a]ny disputes under this agreement shall be resolved in San Juan under the rules of the American Arbitration Association.”

[*34] Early in 1996, PCS authorized Romulus to bid slightly over $18,000,000 ($18,006,000, to be precise) to acquire an FCC license in the Norfolk, Virginia market. Romulus, acting through one of its principals, defendant-appellant Anthony Terence Easton, mistakenly entered a bid for $180,060,000 on PCS’s behalf. In the aftermath of this debacle, Ea-ston, eager to avoid the penalties incident to the withdrawal of the inflated bid, attempted to persuade the FCC that it, rather than Romulus, had committed the bevue. The attempt backfired when the FCC concluded that Easton had intentionally misrepresented material facts, and levied hefty fines against PCS for the bidding error and Easton’s botched cover-up.

The plaintiffs sued Romulus, Easton, and Easton’s spouse in a local Puerto Rico court, alleging fraud, breach of contract, and breach of fiduciary duty. Romulus countered by filing a demand for arbitration with the American Arbitration Association (the AAA) and moved to dismiss the court action on the strength of the Service Agreement’s arbitration clause. This motion remains outstanding.

The AAA agreed to hear the dispute, notwithstanding the plaintiffs’ objection. The plaintiffs then commenced a second action in Puerto Rico’s federal district court, seeking both a declaration that the dispute was not arbitrable and a provisional order staying arbitration pendente lite. The plaintiffs’ complaint premised subject matter jurisdiction expressly and solely on the FAA. The court below granted interim relief and ordered the AAA—whom the plaintiffs had named as an additional defendant—“to stay all proceedings in the case ... until this Court makes an adjudication as to the arbi-trability of the matters brought before it.” This appeal followed.

Because the district court’s stay order is in the nature of an injunction, we have appellate jurisdiction. ' See 9 U.S.C. § 16(a)(2) (authorizing an immediate appeal from “an interlocutory order granting ... an injunction against an arbitration that is subject to this title”); see also 28 U.S.C. § 1292(a)(1) (1994) (permitting interlocutory appeals from injunctions).

The central issue on appeal is whether the lower court had subject matter jurisdiction over the parties’ dispute. This issue turns on an application of 28 U.S.C. § 1331 (1994), which grants federal district courts original jurisdiction over civil actions “arising under the Constitution, laws, or treaties of the United States.” Because no other source of jurisdiction appears on the face of the complaint, we must ask whether PCS’s suit can be said to “aris[e] under” federal law within the meaning of section 1331. See Viqueira v. First Bank, 140 F.3d 12, 17 (1st Cir.1998).

It is settled beyond peradventure that a federal court must determine the existence of federal question jurisdiction according to the well-pleaded complaint rule. See id. The rule stipulates that, with few exceptions (none applicable here), a case arises under federal law only if a federally cognizable cause of action appears within the four corners of the complaint. See City of Chicago v. International College of Surgeons, — U.S. -,-, 118 S.Ct. 523, 529, 139 L.Ed.2d 525 (1997); BIW Deceived v. Local S6, 132 F.3d 824, 831 (1st Cir.1997). Here, the complaint’s jurisdictional allegations rest singularly on the FAA, and the claims asserted sound exclusively in tort and contract— causes of action rooted in local law. Accordingly, federal jurisdiction depends on the FAA—and the FAA cannot support such a weight.

The Supreme Court has concluded that the FAA “is something of an anomaly in the field of federal-court jurisdiction” because it “creates a body of federal substantive law” without simultaneously “creat[ing] any independent federal-question jurisdiction under 28 U.S.C. § 1331 or otherwise.” Moses H. Cone Memorial Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 25 n. 32, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983). As a result of this odd configuration, there must be some independent basis for federal jurisdiction—say, admiralty or diversity of citizenship—before a suit aimed at compelling arbitration can proceed in federal court. See id.

[*35] To be sure, the case at hand presents ‘ a slightly different question from that considered by the Moses H. Cone Court in that PCS seeks an order staying arbitration as opposed to an order compelling arbitration. We deem this to be a distinction without a difference. We have held squarely that the power to enjoin an arbitration is “the concomitant of the power to compel arbitration,” Societe Generate de Surveillance, S.A. v. Raytheon European Mgmt. & Sys. Co., 643 F.2d 863, 868 (1st Cir.1981), and thus the same provision of the FAA, 9 U.S.C. § 4, authorizes both types of orders. Since the Court’s interpretation of section 4 in the context of an order compelling arbitration is clear and unambiguous, there is no principled way in which we can deviate from that interpretation in the context of an order staying arbitration. We hold, therefore, that a suit under the FAA either to stay or to compel arbitration must proceed in a state forum unless some independent basis for federal jurisdiction exists. ^[1] Accord Westmoreland Capital Corp. v. Findlay, 100 F.3d 263, 268 (2d Cir.1996).

The plaintiffs have a fallback position, but it is feeble. They suggest on appeal (though not in them complaint) that section 503(b) of the Communications Act of 1934, 47 U.S.C. § 503(b), furnishes a hook on which federal subject matter jurisdiction can be hung. ^[2] We disagree.

In the first place, “[i]t is black-letter law that jurisdiction must be apparent from the face of the plaintiffs’ pleading,” Viqueira, 140 F.3d at 18, and the plaintiffs’ complaint does not mention 47 U.S.C. § 503(b). Moreover, even were this statute mentioned in passing, it would fail to supply the requisite independent basis for federal jurisdiction. We explain briefly.

It is true, as the plaintiffs assert, that this case peripherally involves FCC bidding practices, and that cases sometimes arise under federal law when an interpretation of federal law is outcome-determinative. See Smith v. Kansas City Title & Trust Co., 255 U.S. 180, 199, 41 S.Ct. 243, 65 L.Ed. 577 (1921). But section 503(b) of the Communications Act confers no private right of action, and the plaintiffs’ complaint only advances non-federal claims. Consequently, while an interpretation of section 503(b) might implicate limited aspects of the plaintiffs’ tort and contract claims, this is too tenuous a connection to support a claim of federal jurisdiction.

No less an authority than the Supreme Court has made this clear. Unless a federal statute bestows a private right of action, courts ought to presume that Congress did not intend the statute to confer federal jurisdiction. See Merrell Dow Pharm. Inc. v. Thompson, 478 U.S. 804, 814 & n. 12, 106 S.Ct. 3229, 92 L.Ed.2d 650 (1986). Hence, “the presence of [a] federal issue as an element of [a] state tort is not the •kind of adjudication for which jurisdiction would serve congressional purposes and the federal system.” Id. at 814, 106 S.Ct. 3229. It follows inexorably that, because the claims asserted in the plaintiffs’ complaint do not themselves emanate from federal law, the plaintiffs cannot predicate federal jurisdiction on section 503(b) of the Communications Act.

We need go no further. As neither the FAA nor any other federal statute furnishes an independent basis for federal jurisdiction, the district court lacked authority either to consider the plaintiffs’ complaint or to make any orders in respect to the slated arbitration of the parties’ dispute.

The district court’s jurisdictional finding is reversed, the 'stay order is vacated, and the cause is remanded with instructions to dismiss the action without prejudice for ivant of [*36] subject matter jurisdiction. Costs in favor of the appellants.