ATLANTA  Three weeks after temporarily sparing a Georgia inmate from the death penalty, the United States Supreme Court on Tuesday declined to hear his appeal, a decision that will probably lead to a quick execution.

The inmate, Troy A. Davis, 40, was convicted in 1991 of murdering Mark A. MacPhail, a Savannah police officer. The court’s decision, made without comment or explanation, allows Georgia officials to obtain a new death warrant and schedule the execution, probably in the next few days or weeks.

The case has led to an outpouring of support for Mr. Davis, largely because seven of nine witnesses against him have recanted their testimony, with two claiming that the police had pressured them to testify against him. Prosecutors presented no physical evidence and no murder weapon, and three witnesses have said another man admitted to the murder.

World leaders including former President Jimmy Carter, Archbishop Desmond Tutu of South Africa and Pope Benedict XVI have challenged the fairness of Mr. Davis’s conviction.