President Donald Trump said Sunday that Sen. Lindsey Graham called him just hours before his death to discuss advancing the SAVE America Act, saying the South Carolina Republican sounded tired after returning from Ukraine but otherwise appeared to be in good spirits.

"What makes it even stranger is I got a call last night some time in the early evening, maybe in the sevens, and he called and he said we're all set for the Save America Act," Trump said. "He was pushing the SAVE America Act like crazy."

Speaking by phone on NBC's "Meet the Press," Trump said Graham's final call underscored the late senator's relentless work ethic and devotion to public service.

Graham, who died Saturday night after what was described as a brief and sudden illness, had just returned from a trip to Ukraine, Trump said.

"He said he just landed from Ukraine. That's a long trip to make. He sounded a little tired, but perfect," Trump said. "He actually said he was tired, but he wanted to pass the SAVE America Act, and I said, 'Well, we'll get it done, Lindsey. I'll get it done. I'll see you soon. We might even meet today.'"

Trump said he received word of Graham's death several hours later.

"It couldn't have been much longer. It could have been his last call. I don't know exactly, but I got a message at about 1:00 in the morning from one of the people in his office that he had passed away," Trump said. "I said, I can't believe it. He was like a member of the family to me. It's very tough, actually."

The president said Graham had a unique ability to work across party lines and accomplish difficult legislative goals.

"He was such an advocate," Trump said. "If he wanted to get something, and you know, he had a unique ability. He was able to deal with Democrats. If I had a problem, a real problem, I wouldn't often ask, but if I had a problem with a Democrat, he could work it out. He was a great politician, actually."

Trump said Graham loved serving in the Senate and had been poised to win another term.

"There was nobody like him," Trump said. "He loved being a politician, and he was going to win his election. He was going to win it big."

While acknowledging Graham could be combative when pursuing issues he believed in, Trump said the senator earned widespread respect.

"He was a tough cookie. Don't misunderstand," Trump said. "If he wanted to get something, if he thought he was right and had people against him, he could be very tough, actually, but he was a good person."

Asked whether Graham had mentioned feeling ill during their conversation, Trump said the senator indicated only that he was tired from traveling.

"He told me, 'You know, I feel good, but I'm tired,'" Trump said. "He was fine. I knew him well. He would let you know if he wasn't feeling well."

Trump said Graham's death appeared to have come suddenly.

"It had to be something like that that would just be a quick end," Trump said. "Other than being tired, he was fine."

Reflecting on Graham's Senate career, Trump singled out the senator's impassioned defense of Supreme Court Justice Brett Kavanaugh during his 2018 confirmation hearings.

"His moment on Kavanaugh was one of the classics in the history of the Senate," Trump said. "I think that saved Brett Kavanaugh's Supreme Court ascension."

Trump also recalled how his relationship with Graham evolved after they competed during the 2016 Republican presidential primary.

"We got friendly, and the friendship grew," Trump said. "He was an amazing advocate. I don't know how you find anybody like him."

The president said Graham frequently visited the White House and served as a trusted barometer of Senate sentiment.

"He was a great gauge, a temperature gauge, of the Senate," Trump said. "He was somebody that most Democrats liked, some didn't, but most Democrats liked, and just about all of the Republicans liked Lindsey."

Asked about who should replace Graham in the Senate, Trump said he already has someone in mind but declined to identify the person, saying it was "too soon with Lindsey."

"I have someone that I think would be great, but I don't want to say it now because it's too soon with Lindsey," Trump said. "I don't want to even talk about anybody."

Instead, Trump praised South Carolina Gov. Henry McMaster, saying he trusted the Republican governor to make the interim appointment before voters choose a successor in a special election.

"The governor is a good friend of mine," Trump said. "I endorsed him early on, and he endorsed me right from the beginning."

Trump recalled that McMaster, then South Carolina's lieutenant governor, was among his earliest supporters during the 2016 Republican presidential campaign. He also pointed to his decision to appoint then-Gov. Nikki Haley as U.S. ambassador to the United Nations, a move that elevated McMaster to the governor's office.

"By moving her, I got myself a great guy," Trump said. "Henry McMaster has been a really good governor, and a really good guy. ... He's going to do the right thing, I think."

Trump said McMaster would make "a good decision" on the interim appointment but noted that South Carolina voters would ultimately choose Graham's successor in a special election.

"Ultimately, there will be an election," Trump said. "I have someone that I like, but I'm not going to tell you now because it's too soon."

The president ended the interview by again praising Graham's contributions to the country, particularly his role in securing Kavanaugh's confirmation.

"He's got so many legacies," Trump said. "He was somebody that loved our country, and he fought very hard for the country."