The 42nd president's remarks echo those made by Lynch on Friday, who acknowledged that the meeting has cast a "shadow" over the Justice Department's investigation into a private email server
used by Hillary Clinton while she was leading the State Department. The criticism of the meeting prompted Lynch to say Friday that she will accept the determinations and findings of the FBI and career prosecutors who are investigating Clinton's email use.
"The President's conversation with the attorney general was unplanned and was entirely social in nature. But recognizing how others could take another view of it, he agrees with the attorney general that he would not do it again," an aide to Bill Clinton told CNN Saturday.
Hillary Clinton weighed in on the meeting as well Saturday, telling MSNBC's Chuck Todd, "Obviously, no one wants to see any untoward conclusions drawn, and they said they would not do it again."
Bill Clinton and Lynch met privately on Monday. Clinton, who had been in the Phoenix area earlier in the day for a fundraiser for his wife's campaign, according to a campaign source, joined Lynch aboard her plane while both were on the tarmac at Phoenix Sky Harbor International Airport.
"I certainly wouldn't do it again because I think it has cast this shadow over what it should not, over what it will not touch," Lynch said Friday at the Aspen Ideas Festival, adding, "It's important to make it clear that that meeting with President Clinton does not have a bearing on how this matter will be reviewed and resolved."
Lynch said the pair mostly talked about grandchildren and a little golf.
"It really was a social meeting, and it was, it really was in that regard," she said. "He spoke to me, he spoke to my husband for some time on the plane, and then we moved on."
But she said she understood why the incident caused concerns, and said it was "painful" to her that the Justice Department's integrity was called into question.
"No matter how I viewed it, I understand how people view it," she said.
The meeting instantly drew criticism from Republicans and even some Democrats, who said that just the decision for the two to interact was a mistake while the Justice Department is conducting an investigation of Clinton's private email server.
As news broke Friday morning that Lynch would address the elephant in the room at Aspen Ideas, hoards of people left early morning panels to rush to hear her speak.
Lynch was unequivocal in repeating that career prosecutors and investigators -- not political appointees -- would be presenting her with findings from the investigation and recommendations on what to do next.
"I will be accepting their recommendations," she said.
The meeting and its fallout are sure to worry some Democrats who see Clinton as the only candidate standing between Donald Trump and the White House. Not only is the fate of her campaign largely in the hands of the Justice Department, but this was an entirely avoidable incident that hits her on one of her most persistent vulnerabilities -- how voters doubt her trustworthiness
The No. 2 Republican in the Senate, Texas Sen. John Cornyn, called for a special counsel Thursday to take over the investigation into the private server, citing the appearance of impropriety.
"This incident does nothing to instill confidence in the American people that her department can fully and fairly conduct this investigation, and that's why a special counsel is needed now more than ever," Cornyn said in a statement.
The conservative legal watchdog group Judicial Watch that has led the charge in suing for access to Hillary Clinton's email records also jumped on the news, calling for an investigation into what transpired between Lynch and Clinton.
"Attorney General Lynch's meeting with President Clinton creates the appearance of a violation of law, ethical standards and good judgment," the group said in a statement. "Attorney General Lynch's decision to breach the well-defined ethical standards of the Department of Justice and the American legal profession is an outrageous abuse of the public's trust."
Presumptive Republican presidential nominee Donald Trump also spotlighted the encounter on the campaign trail and on Twitter.
"Take a look at what happened w/ Bill Clinton. The system is totally rigged. Does anybody really believe that meeting was just a coincidence?" Trump wrote Friday
, in a trio of tweets on the incident Friday morning.
And Democratic Sen. Chris Coons also joined the fray, expressing confidence in Lynch's objectivity but decrying the meeting, even if innocuous, as sending the wrong signal.
"I think she should have said, 'Look, I recognize you have a long record of leadership on fighting crime, but this is not the time for us to have that conversation. After the election is over, I'd welcome your advice,'" Coons told CNN's Alisyn Camerota on "New Day" Thursday.
The White House has maintained that the Justice Department is keeping politics out of the investigation, which is happening at the same time as Hillary Clinton's run for office.
Without commenting directly on Lynch's meeting, White House Press Secretary Josh Earnest reiterated Thursday that President Barack Obama is committed to avoiding "political interference" in Department of Justice investigations, and said Lynch understands investigations should be "conducted free of political influence and consistent with the facts."