Sen. Lindsey Graham said Thursday he had a “cordial, pleasant phone conversation” with presumptive GOP presidential nominee Donald Trump on Wednesday that touched on national security — though Mr. Graham still isn’t endorsing Mr. Trump’s candidacy.

“I congratulated him on winning the Republican nomination for president,” Mr. Graham said in a statement. “I know Mr. Trump is reaching out to many people, throughout the party and the country, to solicit their advice and opinions. I believe this is a wise move on his part.”

Mr. Graham said they had a “good 15-minute discussion” that centered on the national security threats facing the United States.

“I gave him my assessment about where we stand in the fight against [the Islamic State] and the long-term danger posed by the Iranian nuclear deal,” Mr. Graham said. “He asked good questions.”

Mr. Graham, who was one of Mr. Trump’s fiercest critics during the 2016 GOP presidential race, said last week that he would not vote for Mr. Trump or Democratic front-runner Hillary Clinton.

“Finally, my position remains the same regarding both candidates running for president,” Mr. Graham said Thursday. “I will do what I can in the Senate to help the next president. The next president will inherit a mess.”

The disclosure from Mr. Graham came on the same day that Mr. Trump met with GOP leaders in D.C. as the Republican Party tries to unify ahead of November.

In response to Mr. Graham’s comments last week, Mr. Trump issued a blistering statement calling the senator a “poor representative” and “an embarrassment to the great people of South Carolina.”

“Judging by the incompetent way he ran his campaign, it is easy to see why his military strategies have failed so badly — we can’t even beat ISIS!” Mr. Trump said. “While I will unify the party, Lindsey Graham has shown himself to be beyond rehabilitation. And like the voters who rejected him, so will I!”

But in an interview that aired Wednesday evening on Fox News, Mr. Trump predicted that Mr. Graham might ultimately come around, and called him an “honorable person.”

“I think that somebody like Lindsey Graham will end up signing the pledge,” Mr. Trump said on “On the Record with Greta Van Susteren,” referring to a pledge the GOP candidates took to support the party’s eventual nominee. “I actually think he’s an honorable person, and I think he will sign the pledge.”

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