(CNN) A meeting this week between Attorney General Loretta Lynch and former President Bill Clinton is creating headaches for Hillary Clinton's campaign.

Lynch and Bill Clinton met privately in Phoenix Monday after the two realized they were on the same tarmac, an aide to the former president said. The encounter took place ahead of the public release Tuesday morning of the House Benghazi Committee's report on the 2012 attack on a U.S. consulate in Libya.

The meeting is raising questions about whether the independence of the Justice Department, which is conducting an investigation of Hillary Clinton's private email server, might have been compromised.

Presumptive Republican nominee Donald Trump said Thursday the meeting was "terrible."

"It was really a sneak," Trump told conservative talk show host Mike Gallagher . "You see a thing like this and, even in terms of judgment, how bad of judgment is it for him or for her to do this? Who would do this?"

Trump continued his criticism during an interview with New Hampshire-based CNN affiliate WBIN-TV Thursday night, calling the meeting "shocking" and "very disappointing."

Texas Sen. John Cornyn, a Republican, said the incident is why a "Special Counsel" should take over the email investigation

"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.

And Judicial Watch, a conservative legal watchdog group that has sued for access to records pertaining to Hillary Clinton's use of a private email server while leading the State Department, is asking for the Justice Department's inspector general to investigate the meeting.

"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. Her conduct and statements undermine confidence in her ability to objectively investigate and prosecute possible violations of law associated with President Clinton and Secretary Clinton."

Even some Democrats say the optics don't look good.

Sen. Chris Coons, D-Delaware, said he believes Lynch will remain objective in her role but would have advised against the meeting, which he says sends the wrong signal even if it was "a brief, casual, social meeting with the former president."

"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 Thursday on "New Day."

Clinton's campaign hasn't commented on the meeting.

White House Press Secretary Josh Earnest reiterated Thursday President Barack Obama's commitment to avoiding "political interference" in Department of Justice investigations after the airport meeting.

Referring back to Lynch's comments about the meeting, Earnest said Lynch understands investigations should be "conducted free of political influence and consistent with the facts."

He said Obama has also made clear he expects the Department of Justice investigation into Clinton's emails to proceed without political interference.

The huddle could feed into one of the biggest hurdles facing Clinton's campaign: that she's untrustworthy. Clinton herself acknowledged that challenge in unusually direct terms this week.

"I personally know I have work to do on this front," she said in Chicago Monday.

According to a law enforcement official familiar with the matter, the former president saw Lynch's plane on the tarmac and walked onto her aircraft. Lynch's FBI security detail did not stop Clinton and he proceeded to initiate an extended conversation that included discussion of grandchildren. Lynch was surprised to see Clinton walking onto her plane, the official said, and no Justice Department business was discussed.

Speaking at a news conference in Phoenix on Tuesday, Lynch confirmed the meeting and denied the two spoke about any matter pending before the Justice Department or the Benghazi probe. She also said the former president "did not raise anything" about an ongoing case or anything of that nature.

"I did see President Clinton at the Phoenix airport as he was leaving and spoke to myself and my husband on the plane," Lynch said according to CNN affiliate KNXV/ABC15 . "Our conversation was a great deal about grandchildren, it was primarily social about our travels and he mentioned golf he played in Phoenix."

The former president's aide said nothing beyond Lynch's characterization of the account was discussed, and that Clinton "always" extends this courtesy when he is around cabinet secretaries, members of Congress and other dignitaries, pointing to the former president's unplanned meeting with Sen. Ted Cruz at an Alabama airport in May.

Asked in Los Angeles on Wednesday whether the meeting risked the department's impartiality in its investigation, Lynch said the email probe is "being handled by career investigators and career agents who always follow the facts and the law."

Top Democrats on Capitol Hill defended Lynch Thursday.

"All I can say is Loretta Lynch is one of the most outstanding human beings I've ever known," Senate Minority Leader Harry Reid, D-Nevada, told reporters. "Her ethics is above reproach."

Sen. Chuck Schumer, D-New York, called Lynch an "honorable person."

"She has said nothing was discussed related to the investigation so you have two choices: To say this didn't matter or she's lying," Schumer said. "I think it didn't matter. I don't think she's lying."

Of Hillary Clinton, Reid said: "I think she's pretty damn good."