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Garza was sentenced to die for three drug-related murders while head of a major Texas-based marijuana smuggling ring.

WASHINGTON (CNN) -- The 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, 44, is scheduled to be executed Tuesday at the same federal penitentiary in Terre Haute, Indiana, where Timothy McVeigh died by lethal injection last Monday.

The petition argued Garza's jury was improperly instructed on the alternative of sentencing him to life 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.

ALSO Garza attorney John Howley says the Supreme Court and the White House are his client's last hope.     DOCUMENTS Denial of stay of execution in Garza v. Lappin Garza 2nd Supplemental Clemency Memorandum to President Bush Garza 1st Supplemental Clemency Memorandum to President Bush Garza Clemency Petition to former President Clinton Brief for the U.S. in Opposition Documents in PDF format require Adobe Acrobat Reader for viewing.

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The court did not act on a second appeal that contends 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 Seventh Circuit Court of Appeals denied Garza's appeal Thursday, saying the OAS issue should be "addressed to the executive and legislative branches of the government, not the courts."

The Interamerican 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 just 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.

Garza is scheduled to be executed at 7 a.m. local time (8 a.m. EDT) on Tuesday at the same Terre Haute, Indiana, facility where Timothy McVeigh was executed this week.