Dozens of Democratic lawmakers were preparing on Thursday to return to Texas early next week, after fleeing the state to temporarily block Republican leaders from adopting a redrawn congressional map.

The extreme gerrymander could flip five U.S. House seats in the Republicans’ favor, helping the party maintain control of Congress through the end of President Trump’s second term.

The Texas Democrats’ official return could come as early as Monday. For the past few days, the lawmakers have been debating when to leave Illinois, where many of them sought refuge from civil arrest warrants issued by the Texas House.

Some argued for staying out of the state and beyond the reach of Texas authorities into next week, while others lobbied for a return on Saturday, according to two people with knowledge of the deliberations.

On Thursday, State Representative Gene Wu of Houston, who leads Democrats in the Texas House, said in a statement that they had reached a decision as a group: They would return only after the original special legislative session called by Gov. Greg Abbott, a Republican, officially ends on Friday.

Mr. Wu added that they were also waiting until Democratic leaders in California introduced their own congressional map, redrawn to favor Democrats in five additional districts and counteract the Texas proposal. That introduction is expected to happen on Monday.

“We’re prepared to bring this battle back to Texas under the right conditions and to take this fight to the courts,” Mr. Wu wrote, adding, “The fight to protect voting rights has only just begun.”

With their absence, the Texas Democrats prevented a vote on the map by the denying the State House a 100-member quorum it needed.

Mr. Abbott has said he would immediately call a second special session on Friday, and the Republican speaker of the Texas House asked his members to be ready to be in the State Capitol this weekend.

Once a second special session is called, the Republican-favoring map would need to pass several formal legislative hurdles before coming up for a vote. But Republicans were expected to take those steps and adopt the new map as soon as enough Democrats have returned to Austin.