President Trump said on Monday that Gov. Henry McMaster of South Carolina should appoint Senator Lindsey Graham’s sister, Darline Graham Nordone, to finish his Senate term, after Mr. Graham’s death on Saturday.

Mr. Trump wrote in a social media post that appointing Ms. Nordone “would be a fabulous tribute to Lindsey, who loved her dearly!”

Under South Carolina law, the governor can immediately appoint a temporary replacement to complete Mr. Graham’s Senate term. Mr. McMaster, a Republican, has called a news conference at 4 p.m. to announce his pick.

Mr. Graham was running for re-election, seeking his fifth Senate term. He was set to be on the ballot in November.

Mr. Graham and Ms. Nordone shared a close bond. Both of their parents died in a 15-month stretch, leaving Mr. Graham, at 22, to care for his younger sister, who was then 13.

This article will be updated.