(CNN) A former top ethics lawyer in the George W. Bush White House said Thursday that Attorney General Jeff Sessions should leave his post after it was revealed Sessions met twice with the Russian ambassador during the 2016 campaign, then denied it under oath in his confirmation hearings.

"I don't think he can continue as attorney general," Richard Painter told CNN's Chris Cuomo on "New Day." "I don't think he was truthful with the Senate. He did not provide provide full and complete information."

After news of Sessions' contacts with the Russians first broke on Wednesday night, Painter tweeted that the attorney general could come under stricter legal scrutiny.

"Misleading the Senate in sworn testimony about one own contacts with the Russians is a good way to go to jail," he wrote.

Misleading the Senate in sworn testimony about one own contacts with the Russians is a good way to go to jail https://t.co/qH0s6sTMJ9

Sessions has strongly pushed back against the reports, saying he never discussed campaign-related issues with anyone from Russia.

"I never met with any Russian officials to discuss issues of the campaign," he said in a statement Wednesday night. "I have no idea what this allegation is about. It is false."

Asked by NBC News Thursday morning if he would recuse himself in investigating any potential ties between Trump's campaign and Russian officials, Sessions said he would do so "whenever it's appropriate."

Speaking on "New Day," Painter also puzzled over Sessions' initial denial, saying the question posed by Minnesota Sen. Al Franken was not complicated and that Sessions had been misleading in his response.

"He didn't tell the truth," Painter said. "He needed to to disclose the communications that he had with the Russians, if he indeed did have communications with the Russians. That was the clear point of the question."

"This is serious stuff what's going on with the Russians," he added, tying the latest controversy to the dismissal of former national security adviser Michael Flynn, who was asked to resign after news of his conversations with the Russian ambassador before the inauguration were made public.

"We've already had one member of this administration have to resign for lying about contacts with the Russians ... and now we have another one who seems to have trouble telling the truth about what he's saying to the Russians, and that's just not acceptable," Painter said.

Wednesday night, Sessions' spokeswoman, Sarah Isgur Flores, said there had been nothing "misleading about his answer" in his January testimony as he "was asked during the hearing about communications between Russia and the Trump campaign -- not about meetings he took as a senator and a member of the Armed Services Committee."

But Painter said he considered it odd that Sessions, as a member of that particular committee, would be making contact with the Russian ambassador.

"I don't understand why a member of the Senate Armed Services committee is having unilateral discussions with the Russians," he said. "That's a big problem in the Senate Armed Services Committee if that's going on and you have at least one senator (Claire McCaskill) willing to say she's not doing that."

In a tweet Thursday morning, McCaskill, a Missouri Democrat, said: "I've been on the Armed Services Com for 10 years. No call or meeting w/ Russian ambassador. Ever. Ambassadors call members of (the Foreign Relations Committee)."

I've been on the Armed Services Com for 10 years.No call or meeting w/Russian ambassador. Ever. Ambassadors call members of Foreign Rel Com. — Claire McCaskill (@clairecmc) March 2, 2017

McCaskill, however, has also tweeted in the past about discussions with the Russian ambassador.

In January 2013, she wrote: "Off to meeting w/ Russian Ambassador. Upset about the arbitrary/cruel decision to end all US adoptions, even those in process."

Off to meeting w/Russian Ambassador. Upset about the arbitrary/cruel decision to end all US adoptions,even those in process. — Claire McCaskill (@clairecmc) January 30, 2013

Thursday morning, McCaskill acknowledged she met with the Russian ambassador as part of discussions about the Iran nuclear deal and blamed Twitter's character limit on her tweet earlier in the day.

"One-hundred-and-forty characters are tough. The word 'from' should have been in there but I didn't have room," she said, adding that she never had a one-on-one meeting with the ambassador and calling for Sessions to step down.