WASHINGTON — The Supreme Court will take up a momentous fight over parties manipulating electoral districts to gain partisan advantage in a case that could affect the balance of power between Democrats and Republicans across the United States.

At issue is whether Republican lawmakers in Wisconsin drew legislative districts that favored their party and were so out of whack with the state’s political breakdown that they violated the constitutional rights of Democratic voters.

It will be the high court’s first case in more than a decade on what’s known as partisan gerrymandering. A lower court struck down the districts as unconstitutional last year.

The justices won’t hear the arguments until the fall, but the case has already taken on a distinctly ideological, if not partisan, tone. Just 90 minutes after justices announced Monday that they would hear the case, the five more conservative justices voted to halt a lower court’s order to redraw the state’s legislative districts by November, in time for next year’s elections.

The four more liberal justices, named to the court by Democrats, would have let the new line-drawing proceed even as the court considers the issue.