Trump, who has built a huge following with an anti-establishment message, shot back at Ryan in a statement.
"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."
"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," he said.
"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.
The Republican National Committee, under pressure to unify the party or face an electoral rout in the Nov. 8 election, said Ryan and Trump were expected to meet soon. It added that "only a united Republican Party will be able to beat Hillary Clinton."
Many Republicans have grappled this week with whether to support Trump, who has deviated from 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.
Trump's last remaining rivals in the Republican race, U.S. Senator Ted Cruz and Ohio Governor John Kasich, dropped out this week, clearing the New York billionaire's path to be picked as the presidential nominee. His will likely face Clinton, the Democratic front-runner, in the Nov. 8 general election.
