Screenshot/Fox News
Trump also told Fox News host Bill O'Reilly that he wanted Ryan to remain the chairman at the Republican National Convention in July.
O'Reilly asked Trump what would be his "opening statement" to the speaker, ahead of a high-stakes meeting between the two Thursday on Capitol Hill.
"I have a lot of respect for Paul and I think we are going to have a very good meeting, I hope," Trump said. "And I think the big thing is in the history of the Republican Party, nobody has ever gotten more votes than I have gotten in the primaries."
Ryan made headlines last week when he told CNN's Jake Tapper that he was "not ready" to offer his support to Trump until he has proven the ability to unify the party.
Trump said Tuesday that he would be "many millions" of votes ahead of his now-dropped-out competitors by the time the primary season is over. O'Reilly, however, questioned his planned message, countering that Ryan already is aware of his primary success.
"So you are not going to go in and tell him stuff he knows," the Fox News host said. "What are you going to tell him about unifying the party?"
Trump said that he "might repeat it nevertheless because it's an important thing" and brought up the "many people" who have endorsed him.
Apparently unsatisfied with Trump's answer, O'Reilly pressed on. He noted that Ryan was not one of the people who had endorsed Trump.
"I think we're going to have very positive results," Trump said. "And I look frankly for him to stay and be chairman" of the convention.
CNN
The real estate mogul's Tuesday comments to O'Reilly on Tuesday represented a softer stance than earlier statements he made in the aftermath of Ryan's announcement.
He at first did little to hold back in retaliation, as he released a statement Thursday saying he was "not ready" to back the speaker's policy agenda.
The next day, he attributed Ryan's weariness to the real-estate magnate's repeated bashing of 2012 GOP presidential nominee Mitt Romney's performance in the 2012 election. Ryan was Romney's running mate.
"Well they lost a race that should've been won last time, and I've been very open about it,"Trump told "Fox & Friends" in a Friday interview. "That was a race that should've easily been won. That was an easier race than we have this year, but I'll win. You already see the polls going up rapidly."