“It backs up what we’ve been saying, that the Texas Legislature intentionally diminished the rights of Latino voters in particular to elect the candidates of their choice,” Mr. Wilkes said. “We feel that we’ve been vindicated in the courts.”

In a statement, Mr. Paxton praised the parts of the ruling that went in Texas’ favor, but said the invalidation of Districts 27 and 35 was “puzzling considering the Legislature adopted the congressional map the same court itself adopted in 2012, and the Obama-era Department of Justice did not bring any claims against the map.” Spokesmen for Gov. Greg Abbott did not respond to an email requesting comment Tuesday evening.

The judges, for their part, said they had never indicated that the interim maps were suitable for long-term use.

“Although this court had ‘approved’ the maps for use as interim maps, given the severe time constraints it was operating under at the time of their adoption,” the ruling said, that approval was “not based on a full examination of the record or the governing law” and was “subject to revision.”

“Rather than trying to cleanse the plans of continuing discriminatory intent or legal defect,” the judges said, Texas officials’ strategy involved “arguing that the 2011 plans would never go into effect and thus could have no harmful effects, and arguing that the 2013 plans could have no impermissible intent,” even though “there is unquestionably both intent and ongoing effect.” This, they said, was an attempt to prevent the plaintiffs “from obtaining relief for purposeful racial discrimination.”

Gilberto Hinojosa, the chairman of the Texas Democratic Party, said in a statement that the state’s Republican officials had “politically profited from discrimination.”

“It is wrong, and although nothing can fully make it right, we now hope to stop it,” Mr. Hinojosa said. “Texas Democrats look forward to ensuring Texans have fair maps in the remedy hearings to come.”

In addition to the League of United Latin American Citizens, the plaintiffs in the case, which was consolidated from several lawsuits, include the Mexican American Legislative Caucus, the Texas State Conference of N.A.A.C.P. Units, three members of Congress and Texas voters.