Warren Lee Hill's lawyers filed the request Tuesday. They asked the high court in May to review new evidence in the case, and the court is currently scheduled to consider whether to take up his case on Sept. 30.
The state last week scheduled Hill's execution for Monday.
Hill's lawyers have long said he's mentally disabled and therefore shouldn't be executed. The state says Hill's mental disability has not been proven beyond a reasonable doubt.
Hill was serving a life sentence for killing his girlfriend when he was sentenced to die for the 1990 beating death of a fellow inmate.
Copyright 2013 The Associated Press.