In an interview Sunday with CNN's Jake Tapper, Reince Priebus, currently the Republican National Committee chairman, noted that Trump did not admit wrongdoing in the settlement announced Friday.
"When the presidency hits you, and it's at your front door and you realize that you are president of the United States for all Americans, there are some things that are important to you and some things that you decide," Priebus said. "Look, let's move on, we're not admitting wrongdoing, and let's just start leading this country without distraction.
"That's what you're seeing, and I think Americans should look at this as a real positive sign about what kind of great president he is going to be and how he wants to lead this country."
The settlement ended a suit brought by the New York attorney general as well as two class-action suits in California over Trump University. The cases alleged Trump defrauded people who enrolled in real estate seminars he started in 2005.
'Potential conflicts of interest?'
In Sunday's interview, Priebus said Americans shouldn't be concerned with potential pay-to-play schemes in a Trump administration
despite reports that Trump's daughter, Ivanka, who helms part of the family's business portfolio, has sat in on some of Trump's early meetings with foreign leaders.
"We've been at this for a few days. I mean, this is ridiculous. Let's just kind of take a deep breath. The point is, what Americans should see from President-elect Trump is someone who, by being in action from the moment he was declared the winner, he was on a mission to bring everyone together," Priebus said.
"That, to me, is what we should be celebrating. I think people should be encouraged by what they see. And I think it's a real positive sign for the future of our country."
Tapper pressed Priebus on the topic, asking: "As White House chief of staff, you're supposed to look out for any political or ethical minefields. Is it seriously the position of the Trump transition team that this is not a huge cauldron of potential conflicts of interest?"
And Priebus said: "Obviously we will comply with all of those laws, and we will have our White House counsel review all of these things. We will have every 'i' dotted and every 't' crossed, and I can assure the American people that there wouldn't be any wrongdoing or any sort of undue influence over any decision-making."
And he defended Trump's pick for attorney general, Sen. Jeff Sessions
of Alabama, against accusations of racist conduct early in his career. Allegations of racially charged comments cost Sessions a job as a federal judge in 1986.
Priebus said Sessions "started his career fighting George Wallace."
"He voted for (former Attorney General) Eric Holder. He fought for a congressional gold medal for Rosa Parks," Priebus said. "This is an honorable, decent, good human being that we're talking about."
'Sanctuary cities,' immigration
Priebus also suggested the Trump White House could seek to block federal dollars from flowing to "sanctuary cities" that don't enforce immigration laws.
In recent years, local governments across the country fought back against federal immigration enforcement by calling themselves sanctuary cities. Trump made them a focus on the campaign trail, pledging to block funding for cities that take that tack.
"The idea that a city would decide to ignore federal law and then would want the federal government to help them anyway is an inconsistent position for those local governments to continue to engage in," Priebus said.
"And so, I think this is a matter of negotiation ... but certainly I can't imagine that too many Americans are watching this and thinking that it's a good idea for a city to allow for blanket amnesty, ignoring federal law, and then say, 'Now give me $500 million,' " he said. "No, that's not the way life works. And I think that a Trump administration is going to explore this issue and, I think, resolve some of these major problems that are happening all across the country."
Trump has also pledged to reverse President Barack Obama's executive actions on immigration -- throwing into question the legal status of so-called Dreamers who were brought into the United States as children.
Priebus deflected a question on the status of those people, saying Trump would focus on border security and the deportation of those who have committed crimes first. Further immigration policy decisions are "a subject that's going to come up after those first two things are taken care of," he said.