U.S. House Speaker Ryan can't back Trump
"I'm just not ready to do that at this point. I'm not there right now," said the highest-ranked elected Republican.
He called for Mr Trump to unite the party and do more to adhere to conservative principles.
An hour later, the New York businessman responded by saying: "I am not ready to support Speaker Ryan's agenda. Perhaps in the future we can work together."
He hoped he and Mr Ryan could come to an agreement about what is best for the American people, Mr Trump said.
"They have been treated so badly for so long that it is about time for politicians to put them first!"
There has been persistent speculation that Mr Ryan, the 2012 vice-presidential nominee alongside Mitt Romney, may make a last-minute run for the top job.
But he has frequently sought to dispel those claims and did so again on Thursday.
In explaining his refusal to back Mr Trump, he said: "I think what a lot of Republicans want to see is that we have a standard bearer that bears our standards."
In December 2015, Mr Ryan harshly criticised Mr Trump's proposal to ban Muslims from entering the US.
He said it was "not what this party stands for and more importantly it's not what this country stands for".
Although several senior Republicans like Mr Romney have already voiced their objection to the nominee, Mr Ryan is the highest ranked to do so.
Former presidents George W Bush and George H W Bush said on Thursday they would not endorse the controversial presumptive nominee.
Both Bushs, plus former nominees Mr Romney and Senator John McCain, have said they will not go to the party convention in July when Mr Trump will be formally confirmed.
Protests have plagued appearances by Mr Trump, with particular focus on his plan to build a wall on the Mexican border and deport 11 million undocumented immigrants.
Source: BBC News