In an interview with CNN's Jake Tapper, Ryan said he wants Trump to unify "all wings of the Republican Party and the conservative movement" and then run a campaign that will allow Americans to "have something that they're proud to support and proud to be a part of."
"And we've got a ways to go from here to there," Ryan said.
Trump dug in. Hours after Ryan's announcement, Trump declared in a statement that "I am not ready to support Speaker Ryan's agenda." He added, "Perhaps in the future we can work together and come to an agreement about what is best for the American people. They have been treated so badly for so long that it is about time for politicians to put them first!"
Trump continued to highlight Ryan's statements on Friday morning.
"So many great endorsements yesterday, except for Paul Ryan! We must put America first and MAKE AMERICA GREAT AGAIN!" Trump tweeted
On Friday morning, Trump confirmed he intended to meet with Ryan next week, but wasn't sure what they'd talk about.
"I have absolutely no idea," Trump told Fox News' "Fox Friends" about the conversation topics. "There are a lot of days before that."
The developments reflect the growing split in the GOP in the days since Trump's commanding victory in the Indiana primary, which forced his remaining Republican rivals out of the race. The resistance underscored how far he has to go to unite the party before the November general election.
CNN reached out to 16 Republican elected officials, leaders and major fundraisers associated with former Presidents Ronald Reagan, George H.W. Bush, George W. Bush and former Vice President Dick Cheney. Speaking on background, none of them said they were planning to go to this summer's Republican convention. They didn't say they would vote for Democratic front-runner Hillary Clinton. But they said they were not yet supporting Trump.
2012 GOP nominee Mitt Romney declared he'd skip the convention, joining at least three prior Republican nominees -- John McCain and both Presidents Bush -- in declining to attend the event.
Arizona Sen. Jeff Flake told CNN's Manu Raju
that "some of Trump's positions" make it "very difficult for me" to support him.
Meanwhile, Nebraska Sen. Ben Sasse went on a lengthy Facebook diatribe against Trump and conservative blogger Erick Erickson said some members of Congress have joined his effort to recruit a third-party candidate.
Despite the day's tumult, Trump gained some allies, including former Texas Gov. Rick Perry
, his one-time rival in the 2016 race.
"He is not a perfect man. But what I do believe is that he loves this country and he will surround himself with capable, experienced people and he will listen to them," Perry told CNN's Dana Bash.
Bill Cole, a Republican candidate for governor in West Virginia, appeared onstage at a Trump event there Thursday and embraced the real estate mogul's approach to politics, even drawing a comparison.
"You look at the things that I believe Donald Trump brings, and I'm that business guy, too. I'm the one that will go in and make those tough decisions," Cole said.
Taking center stage in the days ahead will be the divide between Trump and Ryan. The speaker's move could help his party's members deflect questions about Trump -- but it also means discord will continue ahead of a general election in which control of the Senate, several governorships and blue-state House seats are also on the line.
The gulf between Ryan and Trump now means Ryan, who as House speaker will chair the Republican National Convention, is months away from coronating a nominee he -- so far -- doesn't officially support.
The first effort at detente between Trump and Ryan, Republican National Committee spokesman Sean Spicer told CNN's Wolf Blitzer on Thursday evening, could come next week. The RNC is attempting to set up a meeting between Trump and Ryan. The speaker's spokesman tweeted that he'd be "happy to attend."
Among the problems: The two aren't on the same page in terms of policy.
On free trade, taxes, immigration, the minimum wage and more, Trump has broken from conservative orthodoxy -- a problem for Capitol Hill Republicans who have prized purity in recent years.
Ryan laid out what he wants to see from Trump in his interview with Tapper.
"Saying we're unified doesn't in and of itself unify us, but actually taking the principles that we all believe in, showing that there's a dedication to those, and running a principled campaign that Republicans can be proud about and that can actually appeal to a majority of Americans -- that, to me, is what it takes to unify this party," the speaker said.
Ryan's comments about Trump quickly became a political football, with Hillary Clinton's presidential campaign highlighting the speaker as part of a "growing list of conservatives rebuking Trump" in an email.
A Republican strategist involved in Senate races told CNN that he's worried Ryan has set up a situation that will be difficult for him to eventually get out of.
"What are the conditions by which Ryan will ever endorse? I don't know how this ends," the strategist said. "What would make him get to a yes on Trump? I'm not sure what Trump can do, other than change his positions."
The speaker's move could help House Republicans -- particularly those facing competitive general election races -- by giving them cover to break from Trump, or delay a stance on whether they'll support him in November.
But many Senate Republicans, including Majority Leader Mitch McConnell, R-Kentucky, and endangered members like New Hampshire's Kelly Ayotte and Ohio's Rob Portman, had already declared on Wednesday that they would keep their commitments to support the party's nominee by backing Trump.
Looming over it all is the prospect of a third-party campaign by a conservative intent on hewing closer to traditional Republican principles than Trump.
Erickson, the conservative blogger, told CNN -- without naming them -- that members of Congress have joined influential Republican members of the #NeverTrump movement in seeking out a candidate.
"Planning is continuing for a third party," he said. "I don't necessarily read this as Ryan endorsing a third party, but it gives motivation to people who want a third party to continue down that track. I have had several congressmen reach out to me to encourage a third party because they are worried about turnout in (November) because they want an alternative to Trump."
The candidate many conservatives view as ideal is Sasse, the freshman Nebraska senator. He has rejected overtures thus far, pointing to his young family and saying like-minded Republicans need to find a candidate who can devote the time necessary to campaigning.
But in a Facebook screed in the early Thursday morning hours, Sasse wrote: "Why shouldn't America draft an honest leader who will focus on 70% solutions for the next four years? You know...an adult?"