Ryan, the speaker of the U.S. House of Representatives, said conservatives wanted to know if Trump shares their values.
"I hope to support our nominee, I hope to support his candidacy fully," Ryan said on CNN. "At this point, I'm just not there right now."
In a statement after Ryan's remarks, Trump shot back: "I am not ready to support Speaker Ryan's agenda. Perhaps in the future we can work together and come to an agreement about what is best for the American people."
The Republican National Committee, asked for a response to Ryan's move, said Ryan and Trump were expected to meet soon. It added that "only a united Republican Party will be able to beat Hillary Clinton."
"We respect Speaker Ryan’s opinion and believe that since the primary ended early we will have time to unify. We anticipate the two meeting soon to begin to help unite the party," said RNC spokeswoman Lindsay Walters.
Trump's remaining rivals in the Republican race dropped out this week, clearing his path to be picked as the presidential nominee. He will likely face Democratic front-runner Hillary Clinton in the Nov. 8 general election.
Many Republicans have grappled this week with whether to support Trump, who has shunned the party line on trade and upset the party establishment with offensive comments about women and immigrants. Trump on Thursday announced a new campaign finance chairman in response to questions about his readiness for a general election race.
"Suppose Trump loses overwhelmingly. Would you want to have been siding with the captain of the Titanic, or maybe seen as someone who was begging the captain to watch out for icebergs?" said Larry Sabato, director of the University of Virginia's Center for Politics.
Ryan criticized Trump in December for proposing to temporarily ban all Muslims from entering the United States and knocked him in March for failing to denounce white supremacist groups during a television interview.
The House speaker, who was the running mate of Republican 2012 presidential nominee Mitt Romney, a harsh Trump critic, said he hoped the party would be unified by this summer but that the pressure was on Trump to do that.
“He won fair and square," Ryan said of Trump, acknowledging his own policy differences with the New York billionaire businessman. He added: "If we don’t unify all wings of the party, we’re not going to win this election."
Ryan repeatedly denied interest in running for president this year despite attempts to draft him by some in his party. He has been putting together a policy plan for House Republicans to campaign on, which he says will be released before the convention in July.
Trump on Thursday began shifting focus from the bruising primary campaign to the general election. He has largely used his own money for his primary fight but plans to follow the more typical path of raising money from outside sources for the general election to succeed Democratic President Barack Obama.
He named his campaign finance chief on Thursday - Steven Mnuchin, a former Goldman Sachs partner who is chief executive of private investment firm Dune Capital Management and with whom Trump worked in a business capacity in the past.
Mnuchin has a long history of political donations, including to Clinton. Since 1998, Mnuchin has given about $71,000 to Democrats, compared with about $37,000 to Republicans. Republicans have questioned Trump's loyalty to the party because he also donated to Democratic candidates in the past.
Trump is hiring staff to equip his campaign for the months ahead and making contact with lawmakers. A Republican congressional aide said there had been discussions about Trump visiting Capitol Hill soon.
U.S. Representative Renee Ellmers, a Republican from North Carolina who has endorsed Trump, told Reuters the campaign would begin raising money for the party.
"They are going to start understanding and realizing that in order to grow this operation, they will need to grow funds, not only for him and for the campaign to beat Hillary Clinton, but for the Republican Party itself," Ellmers said.
Historically, political parties have depended on their nominees to raise money in order to fund their other operations, including working to elect members of the House of Representatives and Senate.
One key worry for Republicans has been that their candidates for Congress and other elective positions could suffer with the divisive figure of Trump at the top of the ticket.
Ron Bonjean, a Republican strategist, said Ryan gave lawmakers in his party cover to steer clear of Trump in their re-election campaigns.
"He is positioning the Republican conference and giving Republicans a message they can hold onto," Bonjean said.