Washington (CNN) Donald Trump came to Capitol Hill Thursday with the hopes of unifying the party, but his heated exchange with one of his fiercest congressional critics overshadowed those efforts.

The presumptive Republican presidential nominee told Arizona GOP Sen. Jeff Flake he would work to defeat him if he didn't change his tune. Flake, who has slammed Trump for his positions on immigration and his racially charged criticism of a Latino judge, reminded Trump that he is not up for re-election until 2018, according to two sources familiar with what occurred.

"It was a bit tense," Flake told CNN Thursday afternoon. "He started out saying that I'd been critical of him, and I have been, frankly, but I think if somebody makes the kind of statements that he's made against the judge from Indiana -- calling him a Mexican in a pejorative way -- and said the things about John McCain that he said, criticizing him for being captured, you know, that's just beyond the pale to diminish the record of John McCain who spent five years as a prisoner of war."

Other members present, however, downplayed the tension during the meeting.

"I think those guys have been pretty blunt in their criticism. And I think what he was attempting to do, in my view anyhow, was to sort of say we all want in the end the same thing," Sen. John Thune of South Dakota, the third-ranking Senate Republican, told CNN about Trump's remarks. "We want constitutionalists on the Supreme Court. We want a conservative agenda for this country. The only way to get that is if we're all working together. He's got his own way of doing that. I thought it was fine."

The meeting unfolded on a dramatic day on Capitol Hill as Trump asked Senate Majority Leader Mitch McConnell to be more supportive of his candidacy and encouraged GOP senators to unite behind him, warning of negative consequences of a divided party.

Trump also huddled with House and Senate Republicans -- including former primary rival Ted Cruz -- Thursday as he seeks to unite Republicans behind his candidacy at time when his campaign is again clouded by controversy.

The clash with Flake contrasted with the goodwill that Trump seemed to engender during his earlier meeting with House Republicans, many of whom said they were encouraged by Trump's more subdued and presidential tone.

The candidate himself downplayed any tensions within the party as he left DC on Thursday. "Had great meetings with Republicans in the House and Senate," Trump tweeted Thursday afternoon. "Very interesting day! These are people who love our country!"

The set of meetings, first with more than 200 Republicans members of the House and then with 41 members of the Senate, are part of Trump's effort to reach out to lawmakers who have been reluctant to get behind his campaign. Though some members are facing difficult races at home because of Trump's controversial rhetoric, the presumptive nominee made an impassioned plea for unity at both gatherings.

During a week when Trump has worried members of his party by veering wildly off message instead of building a coherent case against Hillary Clinton as the FBI wrapped up its investigation into her email use, lawmakers attempted to put the best face on the rifts within the party on Thursday.

Rep. Chris Collins, R-New York, who was one of the first House lawmakers to endorse Trump, said 25 to 30 members lined up to ask questions, and Trump took every one. In a brief gaggle after the meeting, lawmakers supportive of Trump said they felt the meeting was a positive step toward unity.

Rep. Kevin Cramer of North Dakota said Trump repeatedly said "we need to stick together." "He was pleading with us for it," said Cramer, who added he felt that Trump had struck the right tone in the meeting.

The meeting comes as many Republicans on Capitol Hill are trying to come to grips with Trump's freewheeling style -- on display Wednesday night during a speech in Cincinnati in which he reignited a controversy over a tweet some have said is anti-Semitic -- that seems to appeal to many in the GOP base but could turn off the broader electorate heading into the November election.

Many who attended the House meeting said Trump, who was accompanied by his daughter Ivanka and son-in-law Jared Kushner, repeatedly spoke of his desire to unite the party and vowed to accelerate the pace of fundraising for his own effort and congressional races -- which had been a major point of concern for members.

At one point, he turned to Ivanka and asked her to vouch for the fact that he won't "let you down."

Rep. Cresent Hardy of Nevada, who is not going to the Republican National Convention later this month and has not endorsed Trump, asked one of the first questions inside the meeting. He told Trump he was worried about his ability to appeal to the broader electorate during the general election.

Hardy said he represents a district with a large Hispanic, Asian and African-American populations that may be one of the most diverse GOP districts in the country and noted that he is now running against a Latino opponent who is using Trump's comments as a wedge issue.

His question was whether Trump can run a general election campaign that can win over diverse voters without continuing to offend them.

Rep. Peter King, R-New York, said Trump took the time to give a lengthy answer to Hardy's question.

"Trump spent about 10 minutes answering the question -- why he thought he could turn that around," King said. "He was giving examples of some polls where his numbers have gone up, and again, distinguishing between legal and illegal immigration, the importance of jobs. He handled it well. Being in the room, he handled it well."

The tenor of the questions to Trump, several House members said, was polite and respectful.

Members asked about his potential nominees to the Supreme Court, the FBI investigation into Clinton's email practices, his position on trade, and how much he would be campaigning for House members before November.

"He basically said he would be everywhere from now to election day," said King, who has been critical of Trump's candidacy. "It was actually probably Donald Trump at his best."

Several members also said Trump spoke at length about expanding the electoral map -- stating that he could put Oregon, Washington, Michigan and Connecticut in play, even though those states that have long been out of reach for the GOP.

Trump was, however, pressed by the lawmakers about he quickly he could catch up in fundraising -- despite the $51 million haul announced early this week -- as well as how he planned to smooth over some of his more inflammatory rhetoric with key minority groups.

After Trump's address to senators, he met with Cruz for the first since the Texas senator dropped his presidential bid in May. Cruz has not formally endorsed Trump and still has the loyalty of some delegates to the Republican National Convention in July. Republican National Committee Chairman Reince Priebus also attended the meeting between Trump and Cruz.

Later on Thursday, Cruz described his meeting with Trump as "positive and productive." Trump offered him a speaking slot at the convention and he accepted on the spot. A senior Trump official described the meeting as being helpful in mending relations between the two men. Trump did not ask for Cruz's endorsement, and Cruz did not offer his endorsement.

"There was no discussion of any endorsement. He asked me if I would speak at the convention and I said I'd be very glad to do so," Cruz told reporters. "I'm going to urge Americans to get back to the Constitution, to change the path we're on," Cruz added, when asked what he would speak about at the convention. "I'm going to do my very best to point to the policies and principles that we should be unifying behind and that give a better direction for this country going forward."

Trump still hitting his critics

One surprise attendee at Trump's Senate meeting was Sen. Ben Sasse, one of Trump's leading critics in the Senate. Sasse was among the first to emerge from the meeting, but refused to answer questions about what was discussed or whether he was reassured in any way by Trump's comments.

His spokesman later said Sasse went to the meeting "ready to listen."

"Sen. Sasse introduced himself to Mr. Trump and the two had a gracious exchange," Sasse's spokesman said. "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."

Rushing past reporters on his way back to the Hill, South Carolina Sen. Tim Scott said Trump's emphasis was on party unity and that the discussion was a meaty policy session. Trump's tone on the campaign trail, Scott said, was not addressed in the Senate meeting.

Though Trump may be in general election mode, he demonstrated Thursday that he still not risen above calling out his critics -- even if that is not the most politically expedient move at this moment.

Several Republican senators said that Trump singled out GOP Illinois Sen. Mark Kirk for criticism (although other senators said they did not hear it).

Sen. John Thune, R-South Dakota, acknowledged Trump had frank words for Kirk and other GOP critics. "It was kind of exchange you have in the family," Thune said. "I didn't hear him expressing hope (Kirk) would lose. I mean, it was a frank discussion. As I said, that's the kind of discussion you have inside the family."

Kirk told reporters in the Capitol he was aware Trump suggested he would lose his race this fall in Illinois although Kirk disputed that analysis. Kirk, in turn, predicted Trump would do no better than Alan Keyes when he ran for Senate in Illinois against Barack Obama in 2004.

Still, two of Trump's staunch defenders, Tennessee Sen. Bob Corker and Alabama Sen. Jeff Sessions, argued that Trump had accomplished his goals at the meeting by making a more strenuous effort to bring the party together. There was no discussion of the vice presidential selection process during the meeting, they said.

Asked about Trump's inability to stay on message over the past week — particularly his rant in Cincinnati Wednesday night about the six-pointed star controversy and his recent praise for Saddam Hussein's killings of terrorists — Sessions insisted that Trump's points were cutting through.

"Nobody hammered Hillary Clinton more effectively than he did in the past few days," Sessions said. "He gives an hour-long speech on a lot of subjects, so I don't think that's off-message."

Corker also defended Trump's sometimes scattershot approach at his rallies, particularly in a week when Republicans have a chance to skewer Clinton.

"It's just his nature, sometimes he over-explains. His base instincts are very, very good," Corker said after Trump's meeting with senators. "I think people saw that today. They understand that at the base of this, certainly, this is a person that's got tremendous sensitivities and inclusiveness to the entire American people — and I think they see that and know that."

"When you get in these races, you can almost build a caricature of who a person is and I think the more people get to know him, they are going to have a different view of who he is," Corker said. "I thought it was an excellent meeting ... When you just see snippets on TV — or you see one line like you're referring to right now that comes out of a 66-minute speech, people get a very different impression. But I think today, people left feeling great about the meeting, feeling great about the future."

The pro-Trump senators insisted that there were "converts" in the room, but they offered no names.

"They've got a saying in the mountains of Western North Carolina: 'When you learn 'em, you like 'em,'" said Sen. Thom Tillis, R-North Carolina. "With all due respect, I think we've got to cut through the media snippets and into the underlying message and the nerve that he's striking in creating a movement. We've got to recognize that we've got an opportunity to win and transform this nation. I fully believe that Donald Trump is going to help us do that."

But Flake told CNN he was concerned Trump's rhetoric could cost Republicans control of the Senate this year.

"I have said that he certainly needs to change the tone and tenor of the debate so far, but not just that some of the positions and on the Muslim ban, for example, he has walked that back somewhat and that's a good thing," Flake said. "So he has done some things that he needs to do, but these comments, particularly about certain racial groups and, you know, speaking pejoratively about Mexicans too -- it just has no place in politics."

Tillis and Sen. Deb Fischer, R-Nebraska, brushed off suggestions that emotions escalated during the meeting.

"I would say I didn't feel like there was tense exchange anytime in the meeting," Fischer said. "Even with Flake."

Unifying against Clinton

The congressional outreach comes as many Republicans on Capitol Hill are unifying around a strategy to combat Clinton by keeping her email scandal alive to exacerbate voter concerns about her trustworthiness. Republicans on the House Oversight and Government Reform Committee grilled FBI Director James Comey during a hearing Thursday , just two days after he recommended the Justice Department not press charges against Clinton over classified information found on her private email server.

Though he didn't recommend charges, many Republicans believed they'd been handed a gift this week with Comey's denunciation of Clinton's carelessness in her email practices as secretary of state.

But Trump went off message when he took the stage in Cincinnati Wednesday night as he could not resist defending himself from the slights of the "lying," "dishonest" media.

"It's a star, it looks like a sheriff's star," he said indignantly, castigating those who described the shape as anti-Semitic.

Where is the outrage for this Disney book? Is this the 'Star of David' also?

Dishonest media! #Frozen pic.twitter.com/4LJBpSm8xa — Donald J. Trump (@realDonaldTrump) July 7, 2016

To amplify his argument, he noted that his son draws all kinds of stars when he gets home from school and tweeted a photo of a children's sticker book from the Disney movie "Frozen" that featured a star of the same six-pointed shape.

"Where is the outrage for this Disney book? Is this the 'Star of David' also?" Trump tweeted next to the image of Disney princesses Elsa and Anna. "Dishonest media! #Frozen."