Justices Ruth Bader Ginsburg and Sonia Sotomayor said they would not have granted the request.
The practical effect is that this year's elections will almost surely be conducted under the 2016 boundaries, in which Republicans hold 10 of the 13 congressional seats. The GOP domination's of the congressional delegation belies North Carolina's recent history as a battleground state. It has a Democratic governor and attorney general, who have declined to defend the maps.
A three-judge panel last week invalidated the map drawn by the Republican-controlled legislature in 2016, calling it improper partisan gerrymandering. The decision was the first striking down a congressional map on the grounds that it was rigged in favor of a political party.
The court panel ordered lawmakers to redraw the boundaries by Jan. 29.
But the legislative leaders argued that the uniqueness of the court order was the reason the Supreme Court should put it on hold.
The Supreme Court has never thrown out a state's electoral district map because of partisan gerrymandering. It has two cases on its docket that will decide just that question — but they are unlikely to be resolved in time to affect any plan to redraw the North Carolina districts.
The court has already heard a case from Wisconsin and has accepted one from Maryland. In the Wisconsin case, the justices said new district maps did not have to be drawn until the case was decided. In Maryland, challengers lost in a lower court and have appealed, so the single district boundary in dispute has remained in place.
The North Carolina legislative leaders said their state should receive the same consideration as Wisconsin.
"State legislatures should not be forced to draw new maps based on novel theories of unconstitutional partisan gerrymandering unless and until this court concludes that such claims are actually justiciable and identifies a standard for adjudicating them," said the lawmakers' brief.
If the court decides that partisan gerrymandering is not the business of courts, "the tumult of drawing a new map now will have proven completely unnecessary. And if the court announces a new justiciable standard, there is no reason to treat North Carolina any different from Wisconsin or Maryland," they wrote.
The challengers told the Supreme Court it would be unfair to hold another election under the plan.
Lawmakers talk about state sovereignty, the brief for the organization Common Cause said, but "their true motive is as plain as day: the Republican contingent of the legislature wants to enjoy the fruits of their grossly unconstitutional actions for yet another election cycle. That is not a proper reason to seek a stay, let alone grant one."
The League of Women Voters, another group that challenged the plans, noted that Republicans drawing the map stated as one of their goals to retain their political advantage.
The group said in its brief that in the oral argument in the Wisconsin case, Justice Anthony M. Kennedy asked a lawyer for Wisconsin whether it would be legal for those who draw maps to have as an "overriding concern" increasing one party's influence.
"Justice Kennedy's hypothetical is this case," the brief said.
The case is Rucho v. Common Cause.