"These are things that he is going to have to answer for, but I also think there are things from many years ago," Priebus said Sunday on "This Week," responding to a front-page New York Times article looking at Trump's history with women.
"I don't think Donald Trump is being judged based on his personal life," Priebus added. "I think people are judging Donald Trump as to whether or not he's someone that's going to go to Washington and shake things up. And that's why he's doing so well."
Trump responded to The New York Times story on Twitter Sunday morning, dismissing it as a "lame hit piece."
Asked if he thinks Trump is trustworthy, following questions of whether he served as his own spokesperson in the past, Priebus responded, "yes, of course," before adding, "But I also believe that people are entitled to forgiveness and redemption."
Trump also faced more scrutiny this week for not releasing his tax returns, but Priebus said on “This Week” that the presumptive GOP nominee has "rewritten the playbook" on what will matter in the general election.
"I think though that Donald Trump represents such a massive change to how things are done in Washington that people don't look at Donald Trump as to whether or not he releases his taxes," Priebus told ABC News’ Jonathan Karl.
"Here's a guy that's never run for office," Priebus added. "I don't think the traditional playbook applies, Jon. We've been down this road for a year. And it doesn't apply. He's rewritten the playbook."
When pressed on whether Trump should release his tax returns, Priebus said it was "going to be up to the American people… They’re going to have to decide if it’s a big issue or not."
“I got the sense that things are moving in the right direction,” Priebus said. “I would be surprised if he [Ryan] doesn’t get there, because he wants to get there and the things that were -- had taken place on Friday seemed to move the ball a long distance down the field. So I’d be surprised if he doesn’t.”
“I think everyone gets that the process is better in going through the real details of what everyone brings to the table. What does Donald Trump believe? What does Paul believe? And then only after that process, even if it’s a short process, then I think closure is most appropriate then,” Priebus added.
“You can have differences of opinion,” Priebus said. “They don’t have to fall in line 100 percent with the platform… I think these issues are going to be discussed. I think you saw Donald Trump even sort of nuancing some of these positions this past week.”
“When people want to shake up Washington, when people want a more efficient, effective, accountable government, they’re going to have one big question on the ballot: it’s going to be, who’s going to do that?” Priebus said. “Hillary Clinton, who’s a career politician who’s built her entire life and millions and millions of net worth on politics, or a guy who’s never run for office, is an outsider but a businessman that’s going to get something done?”