The justices ordered the three-judge court in San Antonio to come up with new plans, but did not compel the use of maps created by Texas’ Republican-dominated state Legislature. Only Justice Clarence Thomas said he would have gone that far.

Controversy over the maps arose from redrawing political boundaries based on results of the 2010 census that found that Texas had added more than 4 million new residents, mostly Latinos and African-Americans, since 2000. The minority groups complained they were denied sufficient voting power by Republican lawmakers who sought to maximize GOP electoral gains in violation of the landmark Voting Rights Act.

Texas will have 36 seats in the next Congress, a gain of four districts. A divided court in San Antonio drew maps that differed from the Legislature’s efforts, giving Democrats a chance to prevail in three or four more congressional districts. Republicans now represent 23 of the 32 current districts.

The high court said the judges appeared in some instances not to pay enough attention to the state’s choices. The judges made mistakes in their plans, particularly in altering district lines for state legislative and congressional seats in parts of the state where there is no allegation of discrimination on the part of the Legislature, the high court said.

‘‘In the absence of any legal flaw in this respect in the state’s plan, the district court had no basis to modify that plan,’’ the justices said, talking about state House districts in north and east Texas.

The court set no deadline for new maps to emerge from the court in Texas, although state officials have said they need to have something in place by February 1 to hold primary elections, already delayed once, on April 3. The Texas Republican party also has said that Texas may have no voice in the Republican presidential nominating process if the primary is held later than mid-April.

The complicated legal fight over redistricting in Texas is playing out in three federal courts. In addition to the Supreme Court and federal court in San Antonio, a three-judge court in Washington is evaluating the state plans under a key provision of the Voting Rights Act that forces states, mainly in the South, with a history of discrimination in voting to get advance approval before making any changes to the way they conduct elections.

Even without the Washington court’s approval, Texas said it should be able to use its own maps just for this year because time is running short before the primaries.

The minority groups, as well as the Obama administration, say such an outcome is strictly forbidden by the Voting Rights Act and would, in essence, eviscerate the law’s most potent weapon, the advance approval requirement, also known as preclearance.

The justices chose not to allow the state maps to be used without preclearance. But Thomas, who earlier had said he would strike down the advance approval requirement, said Texas’ ‘‘duly enacted redistricting plans should govern the upcoming elections.’’

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