Gov. Henry McMaster of South Carolina, a Republican, plans to call the state legislature back for a special session that will be focused on redrawing the state’s congressional maps, lawmakers said on Wednesday evening. The effort could eliminate the state’s sole Democratic district, held by Representative James E. Clyburn.

Mr. McMaster’s decision came one day after five Republican state senators voted with Democrats to block a resolution that would have brought the legislature back to the State Capitol to consider redistricting.

That vote had seemed to close the door on the matter. Republican lawmakers had considered an agreement to extend their session only when it became clear that Mr. McMaster would not immediately call a special session himself.

But Mr. McMaster, who cannot seek re-election because of term limits, now appears willing to thrust South Carolina into the redistricting battles that have reached fever intensity, particularly in the South, ever since the Supreme Court dealt a blow to the Voting Rights Act last month.

President Trump has been clear about his wish for a G.O.P. sweep of all seven of South Carolina’s congressional districts, pressing Republican officials to draw new district maps before the midterm elections.

Mr. McMaster’s office declined to comment on Wednesday. Recently, he had said that he would let the Republican-controlled General Assembly decide the matter.

If Mr. McMaster calls the special session, lawmakers would face a time crunch. South Carolina’s primaries are on June 9, but early voting begins in two weeks, so Republicans would have to pass new maps before May 26.

The South Carolina House has proposed moving the congressional primaries to August to accommodate new maps.

There are also legal hurdles to consider. Hundreds of overseas voters have already cast ballots, which could prompt lawsuits if their votes are discarded to account for a change of date in congressional elections.

It is still unclear if new maps would pass in a special session, although Republicans control the legislature and would need only a simple majority to approve them.

Davey Hiott, the Republican leader of the South Carolina House, told reporters that his chamber was ready to get things rolling on Friday morning and vote on a map as quickly as possible, ideally next week.

Shane Massey, the Republican leader of the State Senate, who drew national attention for his impassioned speech against redistricting, was much more apprehensive about moving fast. He said public input was important and continued to voice opposition to the redistricting effort.

“I haven’t heard anything that alleviates the concerns, not just for me but for other people that I’ve been talking to,” Mr. Massey said. “The concerns are there. If anything, they’re only heightened.”

He also noted that there were other pressing matters for the legislature to consider in the special session, such as finishing the budget.

Unlike their counterparts in states like Tennessee, Alabama and Louisiana, some South Carolina Republicans have been much more lukewarm about the idea of mid-decade redistricting, mostly because they are skeptical that a new map would guarantee one more Republican-leaning congressional district. Instead, they fear that Democrats could be competitive in the newly created districts as Republican strength in some current districts is diluted.

Mr. Massey said in the chamber on Tuesday that changing the maps was “extremely risky” and could allow Democrats to pick up a seat.

“Very candidly, you’re going to motivate Black turnout, and there will be repercussions from that,” including on local races, he said in that speech.

Mr. Massey and Mr. Hiott did agree that the redistricting debates were about to get even messier in Columbia, the capital.

“It’ll be like nothing we’ve ever seen,” Mr. Hiott said. “It’ll be long. It’ll be tedious. At times, hopefully, it’ll be respectful.”

He laughed when asked what he made of the governor’s change of heart on redistricting, adding, “I never thought it was out of the realm of possibility.”

Mr. Massey said Mr. McMaster had argued in a private meeting that calling the legislature back didn’t mean he was telling them what to do.

“My position on that is, if you’re calling us back, you’re telling everybody what you want us to do,” Mr. Massey said.

Mr. Massey described their redistricting dilemma as “a box within a box,” a “maze,” something he didn’t know how to escape. Sooner or later, he added, they would have to vote on new maps.

The debate over redistricting comes in the waning weeks of a crowded Republican primary battle for governor. All of the leading candidates have expressed their support for redistricting to increase Republicans’ chances of retaining control of Congress. Some of the candidates, including Lt. Gov. Pamela Evette and Alan Wilson, the state attorney general, have showed up at committee hearings, urging lawmakers to move ahead.

Mr. Trump has not yet endorsed anyone in the governor’s race.