President Trump is traveling to Myrtle Beach, S.C., on Friday to drum up support for Senator Darline Graham, his choice in a competitive runoff election to succeed Lindsey Graham in the Senate for a full six-year term.

The trip, announced on Monday by the South Carolina Republican Party, is the latest of many efforts by the president to put his thumb on the scale in a special primary election to replace Mr. Graham after he unexpectedly died in July.

Ms. Graham, the sister of Mr. Graham, will face Representative Ralph Norman, an ultraconservative congressman who has shown a willingness to break from the president’s agenda, in a runoff election scheduled for Aug. 25. At the urging of Mr. Trump, Ms. Graham was appointed to the seat on an interim basis by South Carolina Gov. Henry McMaster.

The South Carolina G.O.P. announced the visit in a statement on Friday, saying the president is “scheduled to hold a rally in Myrtle Beach on behalf of one of the runoff candidates.”

Mr. Trump has gone to great lengths to boost Ms. Graham, a longtime advocate for people with disabilities who had never held political office. He first urged her appointment to serve out the remainder of Mr. Graham’s term, making her the state’s first female senator. Then he gave Ms. Graham his coveted endorsement in the crowded primary election last week for the full six years — passing over a longtime ally in the House, Representative Russell Fry.

Ms. Graham finished in first place in the Aug. 11 special primary election, but not by enough to avoid a runoff against Mr. Norman, who finished in second. After the polls closed that day, Mr. Trump worked the phones to urge high-level officials, including Mr. Fry, to back Ms. Graham publicly.

The president will now travel to Mr. Fry’s district in Myrtle Beach, where Ms. Graham must win over the congressman’s voters to beat Mr. Norman.

It was unclear if the president’s visit indicated that the White House was concerned about Ms. Graham’s political viability. The White House did not respond to requests for information about the event on Friday.