The pair issued a statement after a meeting aimed at unifying a party torn over Mr Trump’s rise to the cusp of the presidential nomination.
It described their meeting as a “very positive step towards unification” that recognised “many important areas of common ground” as well as areas where they disagree.
Mr Ryan has yet to come out in support of Mr Trump, a week after stunning Republicans by withholding his endorsement.
However, their statement suggested both want to crack down on the Republican infighting as they try to pull the GOP together for the fight against Hillary Clinton and Democrats in the autumn.
The much-anticipated meeting unfolded as more Republicans began urging the party to put the extraordinary discord behind it.
“The meeting was great,” Reince Priebus, chairman of the Republican National Committee (RNC), tweeted afterwards.
“It was a very positive step towards party unity.” Mr Priebus attended the opening meeting with the two before Mr Trump and Mr Ryan sat down with a small group of House leaders.
Mr Trump entered the RNC building, the venue a few blocks from the Capitol, through a side door as about a dozen protesters who oppose his immigration positions demonstrated at the front, chanting: “Down, down with deportation. Up, up with liberation.”
They tried to deliver a cardboard coffin to the RNC representing the suffering of immigrants under GOP policies and what they say will be the death of the party under Mr Trump. They were not allowed inside.
Paul Ryan on Trump: "Here's what we agree on. A Hillary Clinton presidency would be a disaster for this country." https://t.co/XglzWIuJSe— CNN (@CNN) May 12, 2016
Mr Trump, for years a registered Democrat, has offended women, Hispanics, and others while violating establishment party orthodoxy on numerous issues Mr Ryan holds dear, from trade to wages to religious freedom.
Trump pulled even with Democratic rival Hillary Clinton in a Reuters/Ipsos opinion poll, in a dramatic early sign that the November 8 presidential election might be more hotly-contested than first thought.
While much can change in the next six months, the results of the online survey are a red flag for the Clinton campaign that the billionaire’s unorthodox bid for the White House cannot be brushed aside.
Trump’s numbers surged after he effectively won the Republican nomination last week, according to the poll.
The national survey found 41% of likely voters supporting Clinton and 40% backing Trump, with 19% undecided. The survey of 1,289 people was conducted over five days and has a credibility interval of 3 percentage points.