President Trump on Friday urged Senator Darline Graham, the South Carolina Republican sworn in this week to finish out the final months of her late brother’s term, to enter the race to succeed him, scrambling what had been shaping up to be a crowded G.O.P. primary for Lindsey Graham’s seat.

“Lindsey was one of the greatest people and Senators I have ever known, and his sister shares his deep love of our Country,” Mr. Trump wrote in a social media post that came not long after he met with Ms. Graham in the Oval Office. “I asked Darline, for the Good of our Nation, to run for the U.S. Senate in the Special Republican Primary on Tuesday, August 11, 2026.”

The endorsement represents a remarkable turn in the race, just days after South Carolina’s governor, prodded by Mr. Trump, appointed Ms. Graham as the interim replacement to fill Mr. Graham’s seat until January, following his sudden death last weekend.

At the time, Ms. Graham, who had been exceptionally close with her brother but had never held elective office, was seen as a caretaker who could serve as a reliable Republican vote while a host of South Carolina G.O.P. politicians jockeyed for the chance to run for a full term. The winner of the compressed special primary would most likely be favored to prevail in the general election in November in solidly conservative South Carolina.

Instead, Mr. Trump’s intervention raised the prospect that Ms. Graham’s interim appointment could become the foundation of a full-fledged Senate campaign with name recognition and incumbency advantages.

If she were to run, Mr. Trump said on Friday, Ms. Graham would have his “Complete and Total Endorsement.”

Several prominent Republicans in the state had indicated that they were weighing bids for the party’s nomination to face Dr. Annie Andrews, the Democratic nominee. The crowd included Representatives Russell Fry, Nancy Mace and Ralph Norman, as well as Lt. Gov. Pamela Evette.

In a state where Mr. Trump’s endorsement remains a powerful force in Republican politics, his backing of Ms. Graham could effectively clear the field for her. But some may stay in the fray, given that the president’s initial choice to win the state’s G.O.P. nomination for governor did not ultimately win.

Currently, Ms. Graham is appointed to serve through Jan. 3, 2027, which would have been the end of her brother’s fourth term. The special primary election to select a nominee to face Dr. Andrews is scheduled for Aug. 11, and the deadline to file for that race is at noon on July 28.

Reid J. Epstein contributed reporting.