Henry McMaster, South Carolina’s governor, appointed Lindsey Graham’s sister, Darline Graham, to replace him in the Senate after his death on Saturday, after Donald Trump recommended that she be given the role.

“Lindsey took care of his little sister in years long departed. It’s my honor to ask his little sister Darline Graham to finish his work for him now,” the Republican governor said as he announced her appointment.

In brief remarks at the event in South Carolina’s capital, Columbia, Darline Graham said: “Lindsey has always been there for me, and now I will be there for him”.

“I promise to work hard over the next several months to support the president and carry forward the efforts of my brother on behalf of the citizens of South Carolina and the United States,” she continued.

“I think this is what Lindsey would have wanted, and I plan to honor him in this way. Now, to Lindsey, I miss you more than I can even put into words, but I’m going to do this. I got it.”

Graham had earlier in the day picked up the support of Trump, who wrote on social media: “I recommended, to Governor Henry McMaster, Lindsey Graham’s wonderful sister, Darline, to serve as interim Senator from the Great State of South Carolina. This would be a fabulous tribute to Lindsey, who loved her dearly!”

A commissioner at the South Carolina Commission for the Blind, Graham was known as having a close relationship with her brother, who became a surrogate father to her after both of their parents died when she was 13 years old.

She had introducedthe senator onstage when he announced his bid for the presidency in 2015, and he later said he thought she could have been a part in his future administration.

“If she took a role on, she would be a great representative of our country. I can’t think of a better person to represent our country in an event than my sister,” Graham told CSPAN.

Asked on CNN about the possibility of Graham taking her brother’s seat in the Senate, John Thune, the majority leader, said the idea “makes a lot of sense” and called it “a way of extending Lindsey’s legacy here, and certainly something that, if that’s what they decide end up doing, I think there’d be a lot of support for”.

Graham will serve as senator until Graham’s term ends in early January.

Republicans will hold a special primary on 11 August to choose a new Senate nominee, who will face off against Democrat Annie Andrews in the November midterms. South Carolina is a strongly Republican state, and analysts believe whoever the party nominates will be favored to win the seat.