WASHINGTON — In a 5-to-4 decision that split along ideological lines, the Supreme Court on Thursday evening rebuffed a request from the Obama administration that it stay the execution of a Mexican citizen on death row in Texas. The inmate, Humberto Leal Garcia Jr., was executed about an hour later.

The administration had asked the court to delay the execution so that Congress might consider recently introduced legislation that would provide fresh hearings on whether the rights of Mr. Leal and about 50 other Mexican citizens on death row in the United States had been violated.

In his last moments, Mr. Leal repeatedly said he was sorry, and shouted twice, “Viva Mexico!” The Associated Press reported.

In 2004, the International Court of Justice in The Hague found that the inmates had been denied their rights under the Vienna Convention. The convention requires that foreigners detained abroad be told they may contact consular officials.

In 2008, the Supreme Court acknowledged that the international court’s ruling was binding but said that the president acting alone could not compel states to comply with it. Congress also had to act, the court said.

On Thursday, in an unsigned majority opinion, the Supreme Court said that Congress had had plenty of time to act and that the court would not now “prohibit a state from carrying out a lawful judgment in light of unenacted legislation.”

“Our task,” the majority wrote, “is to rule on what the law is, not what it might eventually be.”

The majority also noted that “the United States studiously refuses to argue that Leal was prejudiced by the Vienna Convention violation,” suggesting that a fresh hearing would do Mr. Leal no good. He was convicted of kidnapping, raping and killing a 16-year-old girl.

“We decline,” the majority wrote, “to follow the United States’ suggestion of granting a stay to allow Leal to bring a claim based on hypothetical legislation when it cannot even bring itself to say that his attempt to overturn his conviction has any prospect of success.”

Justice Stephen G. Breyer, in a dissent joined by Justices Ruth Bader Ginsburg, Sonia Sotomayor and Elena Kagan, wrote that the government’s request was modest, given that allowing the execution to proceed would, in the solicitor general’s words, “cause irreparable harm” to “foreign-policy interests of the highest order” and endanger Americans traveling abroad.

The court should defer to the executive branch’s assessment, Justice Breyer wrote, as “the Court has long recognized the president’s special constitutionally based authority in matters of foreign relations.”

He proposed issuing “a brief stay until the end of September” to allow Congress time to act.

“In reaching its contrary conclusion,” Justice Breyer wrote, “the Court ignores the appeal of the president in a matter related to foreign affairs, it substitutes its own views about the likelihood of congressional action for the views of executive branch officials who have consulted with members of Congress, and it denies the request by four members of the Court to delay the execution until the Court can discuss the matter at conference in September. In my view, the Court is wrong in each respect.”