Gov. Henry McMaster of South Carolina formally ordered the state legislature on Thursday to return for a special session partly to consider redistricting. But he stopped short of ceding to President Trump’s demands and directly asking for a map that would allow Republicans to sweep the state’s congressional delegation.

Instead, Mr. McMaster’s executive order was consistent with his past statements: that the General Assembly needed to fully debate and examine the matter of redistricting before the midterms in November. That debate, he argued, had not concluded and now required an extra session.

The terse order from Mr. McMaster — after he had previously declined to immediately call for a redistricting session — underscores the tightrope he has tried to walk to appease all factions of his party.

Many Republicans are eager to reconfigure the state’s sole Democratic-held district, represented by James E. Clyburn, to heavily favor Republicans. The leading Republican candidates for governor are echoing those demands, urging lawmakers to help the president retain control of Congress.

But several conservative lawmakers fear that Democrats could be competitive in the newly created districts as Republican strength in some current districts is diluted.

On Tuesday, five Republican state senators voted with Democrats to block a resolution that would have brought the legislature back to the Capitol to consider redistricting. They reasoned that the state’s map was already in compliance with the law, and their vote had seemed to close the door on the effort.

But Mr. McMaster now appears willing to wade 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.

Now, lawmakers 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 a new map before May 26.

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

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

It is still unclear if a new map would pass in a special session, although Republicans control the legislature and would need only a simple majority for approval. Mr. McMaster’s order for a special session also called on lawmakers to pass a budget.

Shane Massey, the Republican leader of the State Senate, who drew national attention for his impassioned speech against redistricting, has continued to voice opposition to the effort.

He said that Mr. McMaster had argued in a private meeting that calling lawmakers 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. McMaster’s announcement comes as other Republican-led Southern states are moving to draw new congressional maps to give conservatives an advantage in areas that have been Democratic strongholds of Black voters.

On Thursday, the Louisiana Senate approved a new map that redrew the Sixth Congressional District to be move favorable to Republicans. Last month’s Supreme Court ruling had specifically deemed the state’s map to be an illegal racial gerrymander. That leaves one majority Black district centered around New Orleans largely intact.

The Louisiana map now has to be taken up by the State House, which is expected to debate it in the coming days.

Emily Cochrane contributed reporting.