At the urging of President Trump, Representative Russell Fry of South Carolina has endorsed Senator Darline Graham after losing his bid in the special primary election on Tuesday to succeed her late brother, Senator Lindsey Graham, according to a person familiar with his thinking.

Mr. Fry iannounced the endorsement on Friday, throwing his weight behind Ms. Graham as she competes in a two-week runoff contest against Representative Ralph Norman, a longtime lawmaker and vice chairman of the ultraconservative House Freedom Caucus, in the solidly Republican state.

Mr. Trump has been heavily involved in the race since Mr. Graham, his longtime ally, died unexpectedly in July. He endorsed Ms. Graham, a disability rights advocate who had never held political office, in the primary election after initially signaling he would support Mr. Fry. The runoff is scheduled for Aug. 25.

The president’s personal interest in the race reflects his close relationship with Mr. Graham and his focus on selecting a loyal ally to replace the late senator — especially in a year when Republicans are concerned about defending their majority in Congress. Although few see the seat at risk of flipping in the deeply red state, Mr. Trump has repeatedly dismissed the prospect of Mr. Norman, who endorsed Nikki Haley for president and is not seen as a reliable ally, filling the seat.

Since polls closed in the primary election on Tuesday, Mr. Trump has been working the phones to drum up support for Ms. Graham, according to three people familiar with the calls who were granted anonymity to discuss private conversations.

That night, Mr. Trump called Mr. Fry to encourage him to endorse Ms. Graham, one of the people said.

Mr. Trump lavished the congressman with praise and stressed that he saw a bright future for him, one of the people said.

Mr. Fry had been torn about whether to endorse Ms. Graham, in part because the bitterly fought primary left a bad taste between the two candidates and their political teams, as both sides sought to sell their alignment with the president, one of the people said. Mr. Fry ultimately decided to prioritize loyalty to the president, the person said.

Mr. Fry called Mr. Trump on Thursday night to discuss the endorsement again. On that call, the person said, Mr. Fry encouraged Mr. Trump to visit the Myrtle Beach area, his hometown, and rally in support of Ms. Graham.