Albert Greenwood Brown, 56, is due to be executed by lethal injection for the 1980 rape and murder of a 15-year-old girl in Riverside.
If the execution occurs, it will be the first in California in nearly five years.
On Friday, U.S. District Judge Jeremy Fogel denied Brown's request to block the execution while Fogel considers a lawsuit challenging the constitutionality of the state's lethal injection protocol.
While denying a stay, Fogel said that Brown must be given a choice of whether the execution would be carried out with just one drug, the sedative sodium thiopental, instead of the usual three.
Brown's lawyers late Friday asked Fogel to reconsider his ruling and to allow both sides to file new briefs today. They argued it is unfair to require Brown to make such a choice when details about a one-drug execution are lacking.
But Fogel in a two-page order said he had already considered the issues raised by Brown.
Fogel wrote "Further briefing would not change the court's ruling and would serve only to delay appellate review of the order in the limited time remaining before Brown is scheduled to be executed."
Brown's lawyers can now appeal to the 9th U.S. Circuit Court of Appeals in San Francisco. The attorneys could not be reached for comment.
Brown also has a deadline set by Fogel of 6 p.m. today to say whether he will opt for the one-drug execution. Fogel said in Friday's order that Brown will not be giving up his right to appeal if he makes that choice.
Brown claims that the three-drug execution procedure has the potential to cause unconstitutional extreme pain.
Brown's lawyers also plan to ask a Marin County Superior Court judge Monday morning to block the execution in connection with a separate lawsuit.
The Superior Court lawsuit claims the state's adoption of the lethal injection protocol violated a California law's requirements for public review of new regulations.