Straining to mend their party after months of chaos, Donald Trump and House Speaker Paul Ryan declared themselves "totally committed" to working together after a fence-mending personal meeting on Thursday. Mr. Ryan praised Trump as "very warm and genuine," and suggested that after initial hesitance he may well end up endorsing the GOP candidate for president.

"We will have policy disputes. There is no two ways about that. The question is, can we unify on the common core principles that make our party?" Ryan said. "And I'm very encouraged that the answer to that question is yes."

Mr. Trump, who used the day to launch a robust charm offensive with members of Congress, broadcast his own enthusiasm, on Twitter and on TV. "I really think we had a great meeting today, and I think we agree on a lot of things and it'll be a little process but it'll come along . I'm pretty sure," he said in an interview recorded for Fox News Channel's "Hannity."

The surprisingly fervent show of unity capped a remarkable week that began with Ryan, the GOP's top elected office-holder and its 2012 vice presidential nominee, turning his back on his party's presumptive presidential nominee just days after Trump had effectively clinched the nomination.

Ryan said at the time he was not yet ready to back Trump, who had succeeded in insulting women, Latinos, disabled people, and many conservatives in the course of a brutal primary season. He also has alarmed the Republican establishment with proposals including deporting millions of immigrants and barring Muslims from the country.

Yet in the days since, many GOP lawmakers – and voters themselves – have made peace with the reality that Trump is their candidate and therefore their only hope of defeating likely Democratic nominee Hillary Clinton. Although some in the GOP fear Trump could spell election disaster and cost Republicans control of the Senate and seats in the House, recent polls have shown a closer race, helping their comfort level.

Ryan himself insisted from the beginning that his only goal was real party unity. His allies in the House have predicted he will get behind Trump in the end, and on Thursday Ryan sounded like he was well on his way.

"We talked about what it takes to unify, where our differences were and how we can bridge these gaps going forward," Ryan said, praising Trump's "unparalleled" accomplishment in getting more votes already than any Republican presidential candidate in history – 10.9 million even before California and New Jersey vote in June.

The two discussed "core principles" including limited government, the Constitution, separation of powers and pro-life philosophy, Ryan said.

Asked whether he would be endorsing Trump a week after his refusal to do so shocked the GOP, Ryan said: "Yeah, I think this is going in a positive direction. And I think this was a first, very encouraging meeting."

The two also issued a joint statement in which they pledged to work together to beat Ms. Clinton.

Trump, 69, and Ryan, 46, would make one of the oddest of political odd couples, one a brash and unpredictable billionaire with a malleable political philosophy and tendency to insult all comers, the other a wonky if telegenic Midwestern conservative dedicated to paring back entitlements and with a big-tent view of the GOP. Like many political partnerships this one would be driven by necessity and a common foe, Clinton, whose candidacy is proving a powerful incentive to Republicans of all kinds to bury their differences.

Trump also met with other House GOP leaders, as well as Senate Majority Leader Mitch McConnell and his top deputies, and senators were later full of praise and offers of help.

Sen. John Cornyn said he invited Trump to come to Texas and offered to help him with Latino voters.

"I was fortunate enough to win the Hispanic vote in 2014. I said I'd be glad to share with you my experience and observations because that's an important part of the voters in 2016," Mr. Cornyn said.

"I've always been impressed but I was really impressed today," said Sen. Orrin Hatch of Utah, adding they discussed the Supreme Court, an important issue for conservatives who've questioned whether they can trust Trump to appoint judges who would ratify their philosophy.

Even Sen. Lindsey Graham, who has called Trump a "nut job" and a "loser as a person," softened his stance after speaking with the candidate by telephone Wednesday.

Mr. Graham, R-S.C., described the billionaire as funny and cordial and said he asked insightful questions about national security.

"He's from New York. He obviously can take a punch," said Graham, who waged his own unsuccessful bid for his party's nomination. He said he still won't endorse Trump but his barrage of "insults will stop."

Trump, in a black SUV, slipped from one GOP power center to another on his fence-mending mission made necessary by his outsider status in a city that embodies insiders.

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About a dozen protesters who oppose Trump's immigration positions demonstrated at the front of the Republican National Committee building where the men met. They chanted "Down, down with deportation. Up, up with liberation."

The scene was similar outside Senate Republican campaign offices where Trump gathered later with McConnell and others. "The GOP is dead to our community," said Deyanira Aldana, 21, a protester who is the child of Hispanic immigrants. "And Donald Trump is the final nail in that coffin."