COLUMBIA, S.C. (AP) - President Donald Trump announced Friday his backing for Darline Graham, sibling of the deceased Lindsey Graham, to seek a complete term succeeding her brother in the Senate.

He posted on social media that she has been a winner throughout her life and, if she chooses to run, receives his full and total endorsement.

Trump added a call for her to enter the race immediately.

The president noted he had talked over a possible campaign with Darline Graham during a White House visit. Four individuals aware of the talks, who could not speak publicly, had earlier indicated she had privately shown interest in running.

Trump's endorsement significantly alters the contest to fill Lindsey Graham's seat following his death last weekend. The president had earlier floated possible support for Rep. Russell Fry. Several other prominent figures, including Fry, Rep. Nancy Mace, Rep. Ralph Norman and Lt. Gov. Pamela Evette, have considered entering the race.

The filing window for a special primary opens July 21 and closes July 28, with the primary set for Aug. 11.

Arrangements for Lindsey Graham's funeral were revealed Friday as well. A service will occur in Washington on July 28, followed by additional events in South Carolina on July 29.

South Carolina Gov. Henry McMaster named Darline Graham to complete the rest of her brother's term, which concludes in January.

As the first woman to represent the state in the Senate, Darline Graham described the role as a great honor while many of her brother's staff members and advisers stood behind her, some visibly emotional.

She stated that Lindsey had always supported her and that she would now support him in return.

Lindsey Graham passed away Saturday at age 71. An initial medical examiner report indicated he experienced a tear in his aorta.

He never married or had children, yet his sister frequently joined him at key political moments, speaking at gatherings and appearing in campaign materials. After their parents died when Darline Graham was 13, her older brother became her legal guardian and later adopted her to pass along his military benefits.

By building ties with Darline Graham, who lacks prior political experience yet remained a steady presence in her brother's career, Trump may seek another ally to advance his priorities in the Senate.

Though their relationship had its difficulties at times, Lindsey Graham served as one of Trump's closest Senate advisers, and the day after the death the president called him like family.

In his Monday announcement, McMaster made no mention of Darline Graham serving only temporarily.

Still, a source familiar with the governor's views but not authorized to comment publicly said McMaster had not considered that she might run for the seat herself when making the appointment.

Sen. Tim Scott, another South Carolina Republican, stated he would avoid endorsing anyone in the primary due to his role as chairman of the National Republican Senatorial Committee.

Yet as a South Carolina voter, he noted he could get involved later and praised Darline Graham's strong beginning, questioning why she should not run.

At the time of his death, Lindsey Graham held millions in his campaign fund and was poised to raise far more for the general election. Those resources could not transfer directly to Darline Graham if she runs, according to Bradley A. Smith, a former Federal Election Commission chairman.

Federal rules would restrict Lindsey Graham's campaign to transferring only $2,000 to a Darline Graham bid. Smith noted, however, that unlimited amounts could move to the National Republican Senatorial Committee, which could then spend freely in coordination with her campaign following a recent Supreme Court ruling.

The funds could not be designated specifically for her, yet the party would likely ensure adequate resources, Smith added, now a professor at Capital University Law School in Ohio.

Kim reported from Washington. Associated Press reporter Thomas Beaumont contributed from Des Moines, Iowa.