KELLY, Circuit Judge.

Antonio Caballero filed the underlying lawsuit in the United States District Court for the District of Utah seeking a "judgment on a judgment" he had obtained from a Florida state court. The federal district court registered the Florida state-court judgment under 28 U.S.C. § 1963, but denied all other relief because Mr. Caballero did not establish personal jurisdiction over the defendants. As a result, Mr. Caballero could not utilize federal district court collection procedures. Mr. Caballero then filed a motion to alter or amend the judgment, which the district court denied. He appeals both orders. We exercise jurisdiction under 28 U.S.C. § 1291, and reverse and remand for further proceedings.

I. BACKGROUND

Mr. Caballero sued the defendants in Florida state court, where he obtained a judgment for over $190 million. He then filed the underlying action in Utah federal court alleging that the defendants are Colombian drug traffickers who kidnapped, tortured, and killed his father to facilitate their trafficking and distribution of illicit drugs. The federal complaint further alleged that the defendants, through their agents and representatives, were trafficking millions of dollars of illicit drugs into and through Utah and, further, that their "vicious and vile acts against [Mr. Caballero] and his family were a necessary component part of this scheme." Aplt. App. Vol. 1, at 10.

Mr. Caballero requested a "judgment on a judgment" to have the federal court enter a judgment and authorize collection procedures. His complaint asserted that he "expects to proceed against assets located in Utah pursuant to the Terrorism Risk Insurance Act of 2002, [Pub. L. No. 107-297, § 201(a), 116 Stat. 2322, 2337, codified as a note to 28 U.S.C. § 1610 (TRIA)], and to take discovery as to assets owned by the Defendants or their agencies and instrumentalities." Id. at 9. He served the defendants with process in the federal suit; none of the defendants answered or otherwise participated in the Utah federal action.

The district court registered the judgment under 28 U.S.C. § 1963, despite Mr. Caballero's request to enter a "judgment on a judgment" pursuant to 28 U.S.C. § 1738, and denied all other relief, holding that he had not demonstrated personal jurisdiction over the defendants. Mr. Caballero filed a motion to alter or amend the judgment pursuant to Fed. R. Civ. P. 59(e), seeking to have the court enter a new federal judgment. The district court denied the motion. Mr. Caballero appeals, arguing that § 1963 is limited to registration of a federal judgment in another federal court, and he is entitled to a new judgment, which would allow him to use collection remedies.

II. JURISDICTION AND STANDARDS OF REVIEW

"Federal courts are courts of limited jurisdiction, possessing only that power authorized by Constitution and statute." Gunn v. Minton, 568 U.S. 251, 256, 133 S.Ct. 1059, 185 L.Ed.2d 72 (2013) (internal quotation marks omitted). "Federal subject matter jurisdiction is elemental, and must be established in every cause under review in the federal courts." Safe Streets All. v. Hickenlooper, 859 F.3d 865, 878 (10th Cir. 2017) (brackets and internal quotation marks omitted). The party invoking a federal court's jurisdiction bears the burden of establishing subject-matter jurisdiction. Id. "A court lacking jurisdiction cannot render judgment but must dismiss the cause at any stage of the proceedings in which it becomes apparent that jurisdiction is lacking." Id. (internal quotation marks omitted).

"Questions of statutory interpretation... are pure questions of law that we review de novo." May v. Segovia, 929 F.3d 1223, 1227 (10th Cir. 2019). We also review de novo the legal question of jurisdiction. TransAm Trucking, Inc. v. Fed. Motor Carrier Safety Admin., 808 F.3d 1205, 1210 (10th Cir. 2015). "We review rulings on Rule 59(e) motions for an abuse of discretion. A court abuses its discretion when basing its decision on an erroneous legal conclusion." Nelson v. City of Albuquerque, 921 F.3d 925, 929 (10th Cir. 2019) (citation omitted).

III. DISCUSSION

A. Section 1963

The district court registered the Florida state-court judgment under 28 U.S.C. § 1963, which provides:

Federal courts disagree on whether a state-court judgment may be registered in a federal district court under § 1963. The Seventh Circuit has held that § 1963 does not prohibit removal of a state-court judgment to federal court if other requirements for federal jurisdiction are met. GE Betz, Inc. v. Zee Co., 718 F.3d 615, 625 (7th Cir. 2013). In reaching this conclusion, the court determined that "[r]eading a bar against the enforcement of state-court judgments by federal courts requires reading additional words into § 1963 that are not there." Id. at 624; but see id. at 623-24 (listing "a host of district court decisions" holding that § 1963 does not authorize a federal court to register a state-court judgment (collecting cases)).

In contrast, the Second Circuit found support in § 1963 itself for its view that a new court action must be filed to enforce a judgment entered by a non-federal court. Mobil Cerro Negro, Ltd. v. Bolivarian Republic of Venezuela, 863 F.3d 96, 99 (2d Cir. 2017). "`By its express terms § 1963 applies only to registration of federal-court judgments in another federal court.'" Id. at 123 (quoting Caruso v. Perlow, 440 F.Supp.2d 117, 118 (D. Conn. 2006)) (brackets omitted); see also, e.g., Fox Painting Co. v. NLRB, 16 F.3d 115, 117 (6th Cir. 1994) (finding "unambiguous" § 1963's language specifying the courts whose judgments can be registered in federal district courts)1; Euro-Am. Coal Trading, Inc. v. James Taylor Mining, Inc., 431 F.Supp.2d 705, 708 (E.D. Ky. 2006) ("[T]he registration procedures of 28 U.S.C. § 1963 contain jurisdictional limitations that prohibit federal courts from registering state court judgments.")

We join the courts holding that § 1963 applies only to registration of federal-court judgments in federal courts—not to state-court judgments. Consequently, we reverse the district court's judgment registering the Florida state-court judgment in Utah federal court.

B. Section 1738

We next consider Mr. Caballero's position that 28 U.S.C. § 1738 provides a jurisdictional basis for granting him a "judgment on a judgment." We conclude that it does not.

As relevant here, § 1738 provides:

Section 1738 is a rule of decision, not an independent basis of jurisdiction. "[T]he Full Faith and Credit Clause, in either its constitutional or statutory incarnations, does not give rise to an implied federal cause of action." Thompson v. Thompson, 484 U.S. 174, 182, 108 S.Ct. 513, 98 L.Ed.2d 512 (1988) (citing Minnesota v. N. Sec. Co., 194 U.S. 48, 72, 24 S.Ct. 598, 48 S.Ct. 870 (1904)). In other words, "§ 1738[] has no bearing on the question of whether a district court has subject matter jurisdiction to hear a claim." Vera v. Republic of Cuba, 867 F.3d 310, 320 (2d Cir. 2017); accord Adar v. Smith, 639 F.3d 146, 157 (5th Cir. 2011) (en banc) (holding the Full Faith and Credit Clause "affords a rule of decision in state courts"). Therefore, Mr. Caballero cannot rely on § 1738 to supply federal subject-matter jurisdiction.

C. TRIA

Because Mr. Caballero may not register the Florida state-court judgment in federal district court under § 1963, and § 1738 does not provide a basis for federal jurisdiction, he was required to file a new action in federal district court and establish federal subject-matter jurisdiction over the new action. Although Mr. Caballero filed a new action, he did not demonstrate that the federal district court had subject-matter jurisdiction.

Mr. Caballero's civil cover sheet filed in the district court indicates that the basis of jurisdiction is a federal question. Aplt. App. Vol. 1, at 16. 28 U.S.C. § 1331 provides that federal district courts "shall have original jurisdiction of all civil actions arising under the ... laws ... of the United States." In his complaint, Mr. Caballero stated that he "expects to proceed against assets located in Utah pursuant to the [TRIA], and to take discovery as to assets owned by the Defendants or their agencies and instrumentalities." Aplt. App. Vol. 1, at 9. His opening brief on appeal also relies on § 1331 and the TRIA for jurisdiction. Aplt. Br. at 1.

The TRIA reads as follows:

Pub. L. No. 107-297, § 201(a), 116 Stat. 2322, 2337, codified as a note to 28 U.S.C. § 1610.

"The TRIA provides courts with subject matter jurisdiction over post-judgment execution and attachment proceedings" where the plaintiff has complied with the TRIA's requirements. Vera, 867 F.3d at 321. A judgment creditor may establish federal subject-matter jurisdiction to attach a defendant's property by satisfying the showing required by the TRIA: "(1) [the defendant] is a `terrorist party,' and (2) its assets are `blocked assets.'" Kirschenbaum v. Assa Corp., 934 F.3d 191, 198 (2d Cir. 2019).

Stansell v. Revolutionary Armed Forces of Colombia, 771 F.3d 713, 723 (11th Cir. 2014) (internal quotation marks omitted); see also United States v. All Funds on Deposit with R.J. O'Brien & Assocs., 783 F.3d 607, 615 (7th Cir. 2015) ("[P]er TRIA's text, victims of terror may only execute on `blocked' funds."). In addition, "[i]f the party wishes to execute against the assets of a terrorist party's agency or instrumentality, the party must further establish that the purported agency or instrumentality is actually an agency or instrumentality." Stansell, 771 F.3d at 723 (internal quotation marks omitted); see also id. at 724 (noting that the Foreign Sovereign Immunities Act provides the definition of "agency or instrumentality of a foreign state" (citing 28 U.S.C. § 1603(b))).

Applying these principles to Mr. Caballero's complaint, we determine that it did not establish subject-matter jurisdiction under the TRIA. The complaint did not specifically allege that the defendants are "terrorist parties." Nor did it allege that the defendants' assets are "blocked" as that term is defined in TRIA. As for alleging that the purported agency or instrumentality is actually an agency or instrumentality, the complaint included a section defining the defendants' "agents and instrumentalities" under the TRIA, and stated that Mr. Caballero intended to execute on the Florida state-court judgment against the defendants or their agents and instrumentalities. Aplt. App. Vol. 1, at 12-14.

Mr. Caballero attached the Florida state-court judgment to his complaint. The Florida state court determined that all three defendants were "narco-terrorist organization[s]," id. at 19, the defendants' assets were "`blocked' ... as defined by TRIA," id. at 41, and the defendants acted through many "agents and instrumentalities," a list of which the Florida court appended to its judgment, id. at 30-31. Thus, it appears that Mr. Caballero may be able to establish federal subject-matter jurisdiction under the TRIA if he is permitted to amend his complaint. Consequently, on remand, the district court should permit him the opportunity to amend the complaint.

IV. CONCLUSION

The district court's judgment is reversed and this matter is remanded for further proceedings consistent with this opinion.