A federal appeals court in Atlanta, rejected an appeal by Mr Bush seeking to stop hand recounts in three Florida counties. The decision has no practical effect on the present situation.
These counts were completed last month and part of them included in the official result certifying Mr Bush the winner in Florida by 537 votes. But Mr Bush had not withdrawn his appeal so that he could keep all options open.
The federal court in Atlanta has now refused to give Mr Bush an injunction which would have no effect. The court did not rule on Mr Bush's claim that the counts were unconstitutional.
Texas broke its record for executions in a year when it put to death on Tuesday a convicted killer who confessed to raping and murdering a seven-year-old girl.
The lethal injection of Garry Miller (33), in Huntsville, the state prison, gave Texas 38 executions this year, the most by any state since US authorities began keeping death penalty records in 1930.