The bill is now headed to the Texas House for a vote on the floor. If passed, political analysts say the new map could create as many as five more Republican seats in Congress by shifting seats in major urban centers like Dallas, Austin and Houston. The first steps in that process could begin as early as the beginning of next week.

A Texas House panel on Saturday advanced a draft congressional map aimed at adding five new Republican districts next year over protests from Democrats that the proposal would suppress the votes of people of color.

The full Texas House will now vote next week on a map drawn to flip five House districts to the G.O.P., but Democrats might walk out to deny Republicans a quorum.