GOP lawmakers are saying the Colorado Supreme Court had no authority to throw out districts that they drew up.
Republicans were hoping their map could replace one drawn by a state judge after legislators couldn't agree on boundaries after the 2000 census.
A stay would allow the Republican-drawn map to be used for this fall's general election. That could help Republicans in two hotly contested races in the 3rd and 7th congressional districts.
Last week, three federal judges rejected a separate GOP challenge over the redistricting map, but they stayed there ruling to see if the U.S. Supreme Court takes up the issue.