Attorney General Loretta Lynch spoke in an interview Friday about this week's impromptu half-hour meeting with former President Bill Clinton in Arizona -- a gathering that she said has "cast a shadow" over the Justice Department's investigation into his wife's private email server.

"I certainly wouldn't do it again," Lynch said during an interview at Colorado's Aspen Ideas Festival. "Because I think it has cast a shadow over what it should not - over what it will not touch."

"The most important thing for me as the attorney general is the integrity of this Department of Justice," the attorney general said. "And the fact that the meeting that I had is now casting a shadow over how people are gonna view that work is something I take deeply, and seriously, and painfully."

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Lynch declined, however, to say whether she regretted the tarmac meeting with the former president.

Instead, she said of the appearance of impropriety: "No matter how I viewed it, I understand how people view it."

"It has now cast a shadow over how this case may be received," she said.

CBS News reported early Friday that Lynch would accept the recommendations of career prosecutors in the emails case, though the attorney general stopped short of formally recusing herself from the case.

Lynch reiterated her position at the Aspen festival.

"The matter is being handled by career agents and investigators," she told journalist Jonathan Capehart, noting that those involved are "acting independently -- they follow the law, they follow the facts."

For review, their recommendations will be sent to "career supervisors" at the Justice Department, including senior FBI officials.

"I'll be briefed on it and I will be accepting their recommendations," Lynch said. She added that if she had completely stepped aside for the investigation, she would not even receive briefings on the case.

While she admitted that it's unusual for the DOJ to discuss its investigative process during an open case, the attorney general made an exception because of her meeting with Clinton, husband to the Democratic party's presumptive presidential nominee.

"It's important to talk about how this matter will be resolved and how the review and how the determinations and decisions will be made," Lynch added.

As CBS News has reported, Lynch also confirmed that the decision to accept the recommendations of the DOJ's career investigators had been made prior to her controversial Phoenix airport meeting with Clinton.

"I had already determined that yes, that would be the process," she said.

The attorney general talked about her conversation with the ex-president, describing it as a "social meeting."

"He said hello," Lynch recounted. "I congratulated him on his grandchildren...It led to a conversation on those grandchildren, who do sound great." She added that they also spoke of Clinton's travels in Phoenix.

"It was a social meeting," she said. "It really was in that regard...And then we moved on."