Texas Republicans are moving closer to approving new congressional maps amid a Democratic show of protest over the GOP House speaker’s order that members who fled the state weeks earlier be placed under law enforcement watch.

Democrats said Republicans in the Texas House crossed a line by detaining them en masse and then assigning state troopers to trail them everywhere they go.

The Texas State Capitol was cleared of visitors Tuesday evening and closed to the public after a social media threat, the Texas Department of Public Safety said.

Other Democratic lawmakers have joined a colleague in staying at the Texas Capitol rather than accept around-the-clock police escorts meant to prevent them from blocking a vote on a Republican plan for redrawing congressional districts.

The effort is intended to help the G.O.P. win five more U.S. House seats in the midterm elections. Other states, red and blue, are likely to redraw their own maps.

California state lawmakers have started a series of legislative hearings to advance a partisan plan aimed at winning Democrats five more House seats.

Republicans in the Texas House forced returning Democrats to around-the-clock surveillance by state Department of Public Safety officers to leave the floor.