"The United States cannot afford another four years of the Obama White House, which is what Hillary Clinton represents," Trump and Ryan said in a joint statement after their meeting at the Republican National Committee headquarters near the US Capitol.
The two leaders said they are "totally committed to working together" and called for "shared principles" and a "conservative agenda".
But, in a softening of stance, Ryan on Tuesday had indicated that he may back Trump after getting to know him better.
Trump, 69, emerged as the party's presumptive presidential nominee after winning the Indiana primary in which he defeated Texas Senator Ted Cruz.
Cruz and the other Republican candidate Ohio Governor John Kasich dropped out of the race soon after.
"It is critical that Republicans unite around our shared principles, advance a conservative agenda, and do all we can to win this fall," Trump and Ryan said in their statement, according to which the two leaders had a "great conversation".
"While we are honest about our differences, we recognise that there are also many important areas of common ground," the statement said.
"We will be having additional discussions, but remain confident there is a great opportunity to unify our party and win this fall, and we are totally committed to working together to achieve that goal," it said.
"This was our first meeting, but it was a very positive step toward unification," said the statement, which fell short of a formal endorsement of Trump by Ryan.
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