Attorney General Ken Paxton asked the Texas Supreme Court on Friday to remove 13 Democratic state representatives from office, saying they had abandoned their seats when they fled the state to avoid voting on a redrawn congressional map pushed by President Trump.

Mr. Paxton had warned absent Democrats that he would begin proceedings if enough Democrats did not return to the Texas Capitol to allow a vote on the proposed map, which was designed to flip as many as five Democratic seats in the U.S. House to the Republican Party.

He made good on that threat after the Texas House met for just eight minutes on Friday, long enough to determine that Democrats had ignored the Republicans’ deadline.

Mr. Paxton filed his lawsuit about an hour later, part of an increasingly aggressive effort by Republicans to compel the Democrats’ return. His office said he had focused on 13 Democratic lawmakers — out of more than 50 who did not show up in Austin on Friday — because they had made “incriminating public statements regarding their refusal to return.”

“Something must done,” State Representative Briscoe Cain, a Republican from the Houston area, said, showing the G.O.P.’s mounting frustration. He offered Democrats some unsolicited advice on Gov. Greg Abbott: “I wouldn’t push the governor. He is determined,” he said. “And there’s nothing that’s going to stop him.”

This is a developing story. Check back for updates.

David Montgomery contributed reporting from Austin.