Of the welter of cases on the issue that have moved through the federal courts in recent years, the North Carolina case is perhaps the starkest. The state’s Republican-dominated legislature redrew the House map in 2016 under orders from a different federal court, which had ruled that some districts drawn in 2011 were racially gerrymandered, a practice the Supreme Court has already ruled unconstitutional.

The 2011 map had turned a 7-to-6 Democratic edge in the state’s House delegation to a 9-to-4 Republican one. The redrawn map in 2016 — the one at issue now — produced a 10-to-3 ratio, but the legislature explicitly said that it had been drawn not to disadvantage minority groups, but to hurt Democrats.

“I propose that we draw the maps to give a partisan advantage to 10 Republicans and three Democrats, because I do not believe it’s possible to draw a map with 11 Republicans and two Democrats,” David R. Lewis, a North Carolina state representative who helped lead the remapping, said in 2016.

The three-judge panel ruled in January, though, that the change in motive did not make the map acceptable. It found that the legislature’s intent was “to ‘subordinate’ the interests of non-Republican voters and ‘entrench’ Republican domination of the state’s congressional delegation,” a view they reaffirmed on Monday.

The chief author of the panel’s latest opinion, Judge James J. Wynn of the United States Court of Appeals for the Fourth Circuit, said the legislature’s “invidious partisanship runs contrary to the Constitution’s vesting of the power to elect representatives in ‘the people.’”

The three judges left open, for the moment, what would happen next. They gave the parties in the case until the end of this month to file briefs on whether the court should allow the existing map to be used one more time, in the midterm election, or should order that it be redrawn by mid-September.

With the election less than three months distant, Judge Wynn noted, a court normally would allow one more use of the old map, so as not to disrupt election preparations, especially since North Carolina has already held primaries for the races.