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WASHINGTON (CNN) -- The U.S. Supreme Court Monday rejected one of convicted killer Juan Raul Garza's requests for a stay of execution. His second request is still pending.

Garza is scheduled to be executed Tuesday at the same federal penitentiary in Terre Haute, Indiana, where Timothy McVeigh died by lethal injection last Monday.

Garza's appeal argued that the jury in his case should have been instructed that the only sentence he could have received other than death was life in prison without parole. In a case decided earlier this term, Shafer v. South Carolina, the Supreme Court ruled juries must be clearly apprised of the alternative sentencing.

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The justices rejected Garza's argument without comment.

The court did not act on a second appeal filed by Garza. That appeal argued prosecutors violated an international agreement in the sentencing phase of Garza's murder trial. Garza's attorneys contend the human rights provisions of the Organization of American States charter was violated when evidence was introduced alleging Garza was linked to four murders in Mexico for which he had never been charged. He was convicted on federal charges for committing or ordering three murders in Texas.

The 7th U.S. Circuit Court of Appeals denied Garza's appeal last Thursday, saying the OAS issue should be "addressed to the executive and legislative branches of the government, not the courts."

The Inter-American Commission on Human Rights, in a letter to the U.S. State Department, has urged President Bush to halt the execution.

Garza has also petitioned President Bush for clemency. The clemency petition is largely based on the claim that the federal death penalty is biased against minorities -- Garza is Hispanic, born in Mexico, but a U.S. citizen. The Department of Justice says a recently completed study found no racial bias in the federal system.

Garza's clemency petition also raises the concerns about jury sentencing instructions and international agreements. The Justice Department has opposed all of the Garza appeals.