Washington (CNN) Donald Trump and House Speaker Paul Ryan concluded their highly anticipated meeting Thursday amid signals that the Republican Party will work to piece itself together after a fractious primary.

"While we were honest about our few differences, we recognize that there are also many important areas of common ground," Trump and Ryan said in a joint statement. "We will be having additional discussions, but remain confident there's a great opportunity to unify our party and win this fall, and we are totally committed to working together to achieve that goal."

Ryan, speaking with reporters during his weekly press briefing, sought to portray his openness to Trump, despite withholding his endorsement.

"This is our first meeting, I was very encouraged with this meeting, but this is a process. It takes some time, you don't put it together in 45 minutes," he said.

The speaker called Trump's achievement of earning more votes than any Republican candidate in history "really kind of unparalleled," and clearly hopes to channel the support for the presumptive nominee into support for a conservative policy agenda writ large.

"The question is ... how we unify it all? How do we keep adding and adding and adding voters while not subtracting any voters?" he said. "Most Americans do not like where this country is headed."

Trump tweeted his thoughts while his plane taxied on the runway before taking off for New York, "Great day in D.C. with @SpeakerRyan and Republican leadership. Things working out really well!"

Great day in D.C. with @SpeakerRyan and Republican leadership. Things working out really well! #Trump2016 pic.twitter.com/hfHY9MdAc7 — Donald J. Trump (@realDonaldTrump) May 12, 2016

"I thought it was a great meeting," Trump said in a Thursday evening interview on Fox News with Sean Hannity.

Trump suggested the two sides would eventually come together.

"I don't mind going through a little bit of a slow process," Trump said. "We're getting there."

Republican National Committee Chairman Reince Priebus -- who helped broker the meeting -- told CNN's Dana Bash the meeting was "great," and "a good first step toward unifying our party."

The meeting was great. It was a very positive step toward party unity. — Reince Priebus (@Reince) May 12, 2016

"This was not a usual election, it was a very contentious, tough primary," he said. "I think they had very good chemistry between the two of them."

Speaking later in the day to CNN's Wolf Blitzer, Priebus said Trump and Ryan plan to be back in contact and that could be as soon as Friday.

Senate Majority Leader Mitch McConnell told reporters his meeting with Trump was "constructive" and that they spoke about a "variety of things, both campaign related and issues.

The meeting at RNC headquarters marked a watershed moment.

For Trump, the meeting tested his ability to reconcile with the Washington establishment that he and the voters have scorned.

For Ryan, it will help shape his own future with a party increasingly impatient to get behind its nominee and win back the White House.

A top Trump aide had said there are "no expectations at all" of an immediate Ryan endorsement, describing the Thursday session as an "opening conversation" in an ongoing process of party unification.

Senators who met with Trump said they discussed a range of issues from immigration to tax policy and were impressed at how "genial" and "affable" he was in person. Senate Majority Whip John Cornyn said he understood that Trump is more of a "showman" in public.

He said he suggested to Trump that he find a new way to talk about immigration, and referenced his experience as a border state senator.

"There's some issues that Trump is clear on, but they shouldn't be scary for our members. Our members have always said they believe in ending the lawlessness of illegal immigration and always said we have to have trade agreements that are good," said Sen. Jeff Sessions, the first senator to endorse Trump who has served as a liaison between the campaign and his Senate colleagues.

According to a source familiar with the meeting, Trump told House leadership he would come out with a list, assisted by conservative groups The Federalist Society and the Heritage Foundation, of judicial nominations he would make if he had the opportunity to fill a vacancy on the Supreme Court. Trump also said the members present at the meeting should submit names to him and he would put them on the list.

A few of the House leadership members pushed Trump on abortion -- he has voiced views to the left of the GOP on the issue -- and Trump confirmed repeatedly that he was not interested in changing the party's platform.

The scene

Hordes of reporters mobbed the front entrance of the GOP headquarters and gathered across the street from an alleyway behind the building, but Trump's motorcade evaded the glare of the cameras and led the presumptive GOP nominee to the back entrance.

Inside, Trump was slated for a slew of meetings, the first of which was with Ryan and Priebus, who brokered the meeting in hopes of gluing the GOP's jagged divisions back together after Trump became the presumptive nominee and Ryan dropped a bombshell last week by refusing to back the brash billionaire.

Trump also met with the rest of the House Republican leaders, only one of whom -- Rep. Cathy McMorris Rodgers of Washington -- has not yet endorsed Trump and is holding out alongside Ryan.

Trump then headed to meet with Senate Republican leadership before he departs Washington around 2 p.m.

Democrats, meanwhile, were more than happy to paint Trump and congressional and party GOP leaders as already united.

"I guess he should be giddy about a Trump presidency. Donald Trump is everything that (McConnell) and his party could ever want in a nomination," said Senate Democratic Leader Harry Reid on the Senate floor, adding that Trump's "positions are identical to the Republican Party platform."

Immigration activists and other protesters were on site Thursday morning to reinforce the division Trump has sowed in the country, holding signs calling the presumptive nominee "dangerous," "divisive" and "deceitful." A Trump impersonator with a bullhorn held bags with dollar signs printed on them.

But Priebus left the meeting reassured that Trump would be able to appeal to communities of color that Trump largely alienated during the primary season.

"Tone and tenor matter, and I think Donald Trump understands that, too," Priebus told Blitzer on "The Situation Room," saying that real estate magnate "absolutely" could do well with minority voters.

Assurances

In private and in public, Ryan is sending the message his party wants to hear: The GOP will be united this fall.

In a private meeting in his office Wednesday, Ryan told his colleagues who support Trump that his high-profile sit-down with the billionaire businessman would be the start of a continual dialogue between the speaker's office and the presidential campaign, sources said.

Speaking to the full House GOP Conference in the basement of the Capitol, Ryan suggested that the party's focus this fall will be on defeating Hillary Clinton -- not the internal GOP bloodbath.

"The United States cannot afford another four years of the Obama White House, which is what Hillary Clinton represents," Trump and Ryan said in their statement following the meeting. "That is why it's critical that Republicans unite around our shared principles, advance a conservative agenda, and do all we can to win this fall."

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But according to several allies of the speaker, Ryan went into the meeting seeking some assurances for himself.

He wants to ensure Trump will not hurt his House Republican majority by undermining his colleagues and the carefully crafted election-year agenda the GOP is painstakingly trying to create. He wants Trump to communicate a positive vision, avoid using foul and incendiary rhetoric and keep the party united on its core conservative principles. And as Ryan told reporters Wednesday, he just wants to "get to know" Trump.

Yet, his strategy -- to publicly announce last week he won't yet back Trump -- also has put Ryan on the firing line, including among his own members who say they were blindsided that the leader of their party undermined their presumptive nominee just as the GOP was trying to heal after a divisive primary.

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'Just not ready'

Ryan's revelation to CNN's Jake Tapper that he was "just not ready" to support Trump dominated headlines and put a spotlight on the rift between the real estate mogul and his party.

"Well it sure doesn't make it look like we're all on the same page, does it?" Rep. Mark Amodei, R-Nevada, said of Ryan's public stand. "What's the matter with saying, 'I disagree with him on this and that but we're all wearing the same jersey. So guess what? We want to win the game, and we go have a fight in the locker room.'"

Asked if Ryan's comments bothered him, Amodei said: "Yes, it does. I'm trying to figure out what the upside is."

Rep. Lynn Westmoreland of Georgia, a friend of Ryan's, was surprised by the speaker's lack of endorsement.

"It just seemed like he could have said, "I"m going to support whoever our nominee is that comes out of Cleveland," Westmoreland said. "Why do you want to make mad who you are trying to go into a room and negotiate with?"

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'Competitive'

On the Senate side, McConnell told reporters this week that Trump could be "competitive" in the fall, a show of support from the party leader.

Trump tweeted following his Senate gathering, saying "Great meeting" and including a photo of him talking to McConnell.

Great meeting with @SenateMajLdr Mitch McConnell and Republican leaders in D.C. #Trump2016 pic.twitter.com/R0NuOrZISX — Donald J. Trump (@realDonaldTrump) May 12, 2016

Sen. Shelley Moore Capito, a West Virginia Republican who has not yet said she'll back Trump, said she has a point to make with the front-runner during the Thursday meeting.

"The other thing is the tone that he has had," Capito said. "I'm going to express that I don't think that's a productive tone for the rest of the campaign, and I think it would affect the intensity in which people campaign for him."

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Already, other meetings between Trump and other House factions are in the works, including with the conservative House Freedom Caucus. Many conservatives expect that group and others to get behind Trump. The longer Ryan holds out, the more isolated he could become in his conference.

But Trump's detractors on Capitol Hill believe Ryan has provided cover to his colleagues in tough races by showing some distance from the candidate.

Rep. Carlos Curbelo -- one of the most endangered House Republicans in the country -- said: "I'm very grateful for the speaker for doing this."

After the Trump meeting, Senate GOP leaders briefed their conference in Mansfield room near the Senate floor. Former Trump rival Ted Cruz didn't say much there, other than a joke, according to a senator in the room.

"To be honest with you, I didn't want to come back," Cruz said.

Arizona Sen. John McCain responded: "We didn't want you to either."