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Kamran Jebreili, Associated Press
FILE – Joe Biden, former U.S. Vice President, talks to the U.S. military personnel at an Air Base in United Arab Emirates, Monday, March 7, 2016. Biden said Mitt Romney should run for the Senate, according to news reports of their Friday evening event at Romney's annual retreat that brings together political and business leaders.

PARK CITY — Mitt Romney was encouraged by former Vice President Joe Biden to run for the Senate at Romney's annual retreat that brings together political and business leaders.

"By the way, you should run for Senate," Biden told Romney on Friday evening during their wide-ranging discussion at the E2 Summit on issues including the former vice president's "moonshot" effort to find a cancer cure.

The audience for their exchange, which was closed to the news media, applauded Biden's suggestion, but Rep. Jason Chaffetz, R-Utah, said Romney "just smiled" and offered no response.

Romney and Biden squared off in the 2012 presidential race, when Romney topped the GOP presidential ticket and Biden ran as President Barack Obama's vice president.

But Chaffetz said Romney and Biden encouraged each other "to continue in the public arena" because they "recognize we need good people in government," regardless of party.

"Both gentlemen were very complimentary of each other," Chaffetz said. "I think they get along and have deep respect for each other, so I think it was a natural complement."

Romney has been touted as a candidate for the seat held by Sen. Orrin Hatch, R-Utah, should Hatch decide not to seek an eighth term next year. Hatch said earlier this year he would consider stepping aside for Romney.

Although Hatch called Romney the "perfect" choice to replace him, he also said he didn't expect the two-time presidential candidate to run. Senate Majority Leader Mitch McConnell, R-Ky., has told reporters he's talked with Romney about the race.

Chaffetz, a top Romney surrogate during the 2012 presidential campaign, said Romney would make a "truly superb senator. He's the type of person the Senate needs. It's lacking some leadership."

But the congressman, who is stepping down on June 30 for a position in the private sector believed to be with Fox News, said he doesn't know whether a Senate run is in Romney's future.

"I've heard a lot of chatter but certainly not from him or his family. So I don't know if he's serious about it," Chaffetz said. "He's in a different stage in life. I don't know what his priorities are, how much time and energy he's willing to put into it."

The 225 business leaders at the three-day retreat that ended Saturday are largely donors to Romney's presidential campaign and investors in the private equity firm founded by his son, Tagg, and former top fundraiser Spencer Zwick.

Zwick, who raised some $1 billion for Romney's 2012 White House bid and serves on the board of Hatch's foundation, said he thinks Hatch "is running until he tells us something different."

Romney, who served as governor of Massachusetts after leading the 2002 Winter Olympics in Salt Lake City, told the Deseret News in February he might not be done with politics.

"I don't have any predictions on what I might do. I'm not going to open a door, and I'm not going to close a door. All doors are open," Romney said then, after bringing up the 2018 Senate race.

"I'm not looking forward to anything political at the national level," Romney said. "We've got some races coming up here in Utah that are going to be interesting. We'll see what happens on that front."

Matt Waldrip, the summit's Boston-based executive director, said the rumors he hears about a Senate run for Romney are against Democratic Massachusetts Sen. Elizabeth Warren.

"People, they love him," Waldrip said. "There's a lot of respect for him. He has played a really unique role here at the E2 Summit and that is he's a convener. He has the ability to convene people to talk about the most important things."

He said participants at the retreat spoke about policy in the "context of we're Americans and we're trying to make life better for people. That really was the mood."

The fifth annual retreat featured a number of high-profile speakers, including Romney's 2012 running mate, House Speaker Paul Ryan, R-Wis.; Sen. John McCain, R-Ariz.; Sen. Lindsey Graham, R-S.C.; and Microsoft Chairman John Thompson.

Waldrip said both current and former presidents and vice presidents are always invited.

Longtime Romney supporter Kirk Jowers said the retreat is a "validation to Mitt of the high regard that people still have for him and the influence he still has in our political system."

Jowers noted that the list of presenters included some of President Donald Trump's most strident critics. Romney himself had some of the harshest words for Trump during last year's primary, labeling him a fraud and a phony.

But at the retreat, Jowers said Romney and others chose "not to take the bait and focused on some of the things (Trump) was doing well, and shied away from the easy shots."