Attorney General Loretta Lynch says her private meeting with Bill Clinton was "primarily social." The Clintons haven't commented. (AP File Photo)

(CNSNews.com) - Former President Bill Clinton's private meeting with Attorney General Loretta Lynch not only "looks really bad," but it's typical of the Clintons, said Sen. John Cornyn (R-Texas).

"It's not just the actual impropriety, it's the appearance of impropriety," Cornyn told Fox News's Greta Van Susteren on Thursday evening.

"And it's really part of a larger narrative about the Clintons just acting like the rules that apply to you and everybody else don't apply to them. And certainly I would not have expected Attorney General Lynch, being a professional prosecutor that she is, to make a mistake like this. But it was a very serious mistake.

"I think it undermines public confidence that she's going to be an impartial prosecutor when it comes to the referral from the Department of Justice on the Hillary Clinton email affair. And I think she needs to hand it off to a special prosecutor."

The FBI is still investigating Hillary Clinton's use of a private email server during her tenure as secretary of state, and it will be up to Lynch to decide if the case should be sent to a grand jury.

Van Susteren, an attorney, called the clandestine meeting on a Phoenix airport tarmac "over-the-charts bad."

"I'm not in favor of a special prosecutor," she told Cornyn. "But I think she should make a public statement today removing herself from this investigation and assigning it to her number two who is Sally Yates, a career prosecutor."

Cornyn agreed that might be "a good step," but he said a special, independent counsel would be a better way to go, now that "the independence of the Department of Justic and the Attoreny general herself in this instance is reasonably questioned."

Cornyn also said President Obama, who has endorsed Hillary Clinton as his successor, "does not want this investigation over Hillary Clinton's email to go any further than the FBI."

"We still need to see what the FBI is going to do," Cornyn continued. "I have confidence in Director Comey and the professionalism of the FBI. But I really worry when it comes to the politicization at the Department of Justice. Unfortunately now, Loretta Lynch has just thrown another log on the fire."

President Obama on Thursday refused to answer a question shouted out to him about the Lynch-Bill Clinton meeting, which -- according to Lynch -- was "primarily social." She says Clinton joined her and her husband to discuss their grandchildren, golf and travels.

"There was no discussion on any matter pending before the Department or any matter pending with any other body, there was no discussion of Benghazi, no discussion of State Department emails," Lynch said later, when a reporter asked her about the meeting. "By way of example, I would say it was current news of the day, the Brexit decision and what it would mean," Lynch added.

Sources told Phoenix TV station ABC-15, which broke the story, that the private meeting lasted around 30 minutes.

At the White House on Thursday, spokesman Josh Earnest took multiple questions on the "optics" of the Lynch meeting privately with the husband of a women who is under investigation by Lynch's department.

Earnest repeated the same talking points again and again: "I think the bottom line is simply that both the President and the Attorney General understand how important it is for the Department of Justice to conduct investigations that are free of political interference," Earnest said.

He talked about how "every American citizen should be accountable to the rule of law," and he talked about Lynch's "first-hand experience in conducting public corruption cases," noting that in her former job, she "protected the public trust by prosecuting individuals in both parties who -- where there was evidence to indicate that they may have violated the public trust. This was what earned her strong bipartisan support when she was nominated for the job."

Republican Donald Trump described himself as "flabbergasted" by the inappropriate meeting.

When I first heard that yesterday afternoon, I actually thought they were joking," Trump told Fox News's Sean Hannity Thursday night. "And I am just -- I'm flabbergasted by it. It's amazing. I've never seen anything like that before."