Donald Trump arrives at Republican National Committee headquarters for a meeting with House Republicans on July 7 in Washington. Later in the day, Trump also met with Senate Republicans. (Mark Wilson/Getty Images)

Donald Trump’s private meeting Thursday with Senate Republicans — designed to foster greater party unity ahead of the national convention in Cleveland — grew combative as the presumptive presidential nominee admonished three senators who have been critical of his candidacy and predicted they would lose their reelection bids, according to two Republican officials with direct knowledge of the exchanges.

[Updated story: Trump visits the Hill to mend fences with GOP — and brings his hammer]

Trump’s most tense exchange was with Sen. Jeff Flake (R-Ariz.), who has been vocal in his concerns about the business mogul’s candidacy, especially his rhetoric and policies on immigration that the senator argues alienate many Latino voters and others in Arizona.

When Flake stood up and introduced himself, Trump told him, “You’ve been very critical of me.”

“Yes, I’m the other senator from Arizona — the one who didn’t get captured — and I want to talk to you about statements like that,” Flake responded, according to two Republican officials.

Flake was referencing Trump’s comments last summer about the military service of Sen. John McCain (R-Ariz.), who was a prisoner of war during the Vietnam conflict. Trump questioned whether McCain was a war hero because he was captured.

Flake told Trump that he wants to be able to support him — “I’m not part of the Never Trump movement,” the senator said — but that he remains uncomfortable backing his candidacy, the officials said.

A whole host of influential Republicans have decided not to attend July's Republican National Convention in Cleveland. (Peter Stevenson/The Washington Post)

Trump said at the meeting that he has yet to attack Flake hard but threatened to begin doing so. Flake stood up to Trump by urging him to stop attacking Mexicans. Trump predicted that Flake would lose his reelection, at which point Flake informed Trump that he was not on the ballot this year, the sources said.

Asked in a Senate hallway later about his exchange with Trump, Flake declined to elaborate.

“No, I’ll just leave it,” he told reporters, adding: “My position remains, I want to support the nominee. I really do. I just can’t support him given the things that he’s said.”

Paul Manafort, the Trump campaign’s chairman and senior strategist, who attended the meeting, disputed the characterization of it as contentious.

In a statement to The Washington Post, Manafort said: “Today’s meeting was positive and productive and these characterizations, attributed to unnamed sources, are wholly inaccurate. The conversation was very positive and substantive. The Members were in total agreement with Mr. Trump of the need to unite the Party and work together to win the Presidency and keep a Republican Congress. Mr. Trump was pleased with the discussion and looks forward to working together with the Republican Party leadership towards defeating Hillary Clinton in November.”

Trump also called out Sen. Mark Kirk (R-Ill.) — who withdrew his endorsement of Trump last month, citing the business mogul’s racially based attacks on a federal judge — and said he did not approve of the senator’s action, the officials said.

Characterizing Kirk as a loser, Trump vowed that he would carry Illinois in the general election even though the state traditionally has been solidly Democratic in presidential contests. Kirk did not attend the meeting with Trump.

Asked later in the day about Trump’s comments, Kirk declined to comment other than to say, “I guess he lit me up.”

Trump also singled out Sen. Ben Sasse (R-Neb.), who has refused to support Trump and has emerged as perhaps the most vocal advocate for a third-party candidate. Sasse declined to speak with reporters as he left the meeting.

“Senator Sasse went to today’s meeting ready to listen. Senator Sasse introduced himself to Mr. Trump, and the two had a gracious exchange,” said James Wegmann, the senator’s spokesman. “Mr. Sasse continues to believe that our country is in a bad place and, with these two candidates, this election remains a dumpster fire. Nothing has changed.”

Trump’s trip to Washington on Thursday highlighted the continuing concerns among congressional Republicans over controversial remarks he continues to deliver on the campaign trail and how they may affect GOP members facing tough reelection battles in the fall.

Before his meeting with Senate Republicans, Trump visited with the House GOP conference in what leaders billed as a chance for rank-and-file members to get to know the party’s presumptive presidential nominee.

“What I thought was especially helpful today was our members just got access and got to ask their questions and talk about their issues,” said House Speaker Paul D. Ryan (R-Wis.). “I thought he did a great job engaging with our members, and I think our members appreciated it.”

Ryan said members talked to Trump about the constitutional roles of the president and Congress, reducing regulations and overhauling the tax code — all issues included the “A Better Way” policy blueprint House Republicans have rolled out in recent weeks.

“We clearly have a presumptive nominee who wants to work with us on moving this agenda forward,” Ryan said.

Trump was greeted by applause from more than 200 House GOP members at the standing-room-only gathering, according to GOP aides, and was introduced at the event by financial commentator and TV personality Larry Kudlow. Trump opened the discussion with a speech on the importance of appointing conservative justices to the Supreme Court, members said.

In his discussion with senators, Trump claimed that he had inside intelligence about Hillary Clinton’s vetting process for Supreme Court vacancies and that he knew the names of two people the presumptive Democratic nominee is considering nominating, two Republican officials said. But Trump would not reveal those names.

Trump has long cited vacancies on the Supreme Court as a reason for Republicans to unify behind his candidacy, pledging that he would appoint more-conservative justices than Clinton.

Despite House leaders’ positive statement about the gathering, several GOP lawmakers leaving the morning meeting said they are still unconvinced that Trump can be a good standard-bearer for the party.

“I still need to be persuaded,” said Rep. Charlie Dent (R-Pa.), a moderate member of the conference.

Several lawmakers said questions were raised about derogatory comments Trump has made about minorities and women, as well as his inability to stay on message.

Sheriff Joe Arpaio accused Republicans on June 18 of giving Donald Trump halfhearted endorsements. Is he right? (Peter Stevenson/The Washington Post)

Trump dismissed the issue and insisted he has great support from Hispanics, Dent said.

Rep. Mark Sanford (R-S.C.) left the meeting worried about Trump’s grasp on the basics of the Constitution. At a lunch with reporters afterward, he recalled that the candidate did not seem to know what he was promising to defend.

“I wasn’t particularly impressed,” Sanford said. “It was the normal stream of consciousness that’s long on hyperbole and short on facts. At one point, somebody asked about Article I powers: What will you do to protect them? I think his response was, ‘I want to protect Article I, Article II, Article XII,’ going down the list. There is no Article XII.”

Rep. H. Morgan Griffith (R-Va.), who said he was “uncomfortable” with Trump’s language, gave him a pass on the Constitution flub.

“When he made the comment about the Constitution, I love this article and that article, I assumed he was talking about the amendments, because he was off on the numbers,” he said.

But both Griffith and Sanford tempered their criticism, contrasting Trump’s sometimes slipshod approach to Clinton’s adroit politicking.

“He may be loose on some facts, reckless on some, but there’s not malicious intent there,” Sanford said.

Rep. Adam Kinzinger (R-Ill.) said Trump brought up his recent comments about Saddam Hussein “in the context of how unfair the media has been to him.” Trump has praised the former Iraqi dictator for being “so good” at killing terrorists, while adding that is all he thinks was good about a “bad guy, really bad guy.”

Kinzinger called Trump’s previous comments about Hussein “disgusting and despicable.” He said it was “awkward” to hear the GOP nominee defend his remarks in the room.

Other members expressed confidence that Trump understands he needs to tone down his rhetoric.

“If you look at the trajectory of his unforced errors, he’s getting better,” said Rep. Bill Flores (R-Tex.). “I mean, he’s not where we want him to be, but he’s getting better.”

The gatherings with House and Senate Republicans came after Trump said at a rally in Ohio on Wednesday night that it was a mistake for his campaign to remove a tweet attacking Clinton with a six-pointed star placed on top of a bed of money. The image reportedly appeared last month on an online Web forum frequented by white supremacists and has widely been condemned as anti-Semitic.

The controversy started to quiet by Tuesday as Republicans moved to draw attention to Clinton’s email practices as secretary of state, which had come under investigation by the FBI. But now it has returned to the forefront of the national political debate.

Trump repeatedly said Wednesday that the six-point star was “just a star,” not the Jewish Star of David, and that media outlets that covered the controversy are “racially profiling.”

House members leaving the meeting said Trump did not address the controversy in his remarks and was not asked about it by members.

When asked whether he was bothered by the tweet, Rep. Lee Zeldin (R-N.Y.), the only Jewish Republican in Congress, said, “I don’t think it helps him.”

David Weigel, Paul Kane, Karoun Demirjian and Kelsey Snell contributed to this report.