Senior House Democrats are calling on Attorney General Jeff Sessions to resign after revelations that the former Alabama senator did not disclose meetings he had with the Russian ambassador to the United States during his Cabinet confirmation hearing.

"After lying under oath to Congress about his own communications with the Russians, the Attorney General must resign," House Minority Leader Nancy Pelosi, D-Calif., said in a statement released late Wednesday night, adding that "Sessions is not fit to serve as the top law enforcement officer of our country."

Sen. Ron Wyden, D-Ore., a senior member of the Senate Intelligence Committee, is also demanding a special counsel to investigate the Trump administration for ties to Russia, "given AG Sessions' false statements about contacts with Russia."

And House Oversight and Government Affairs ranking member Elijah Cummings, D-Md., called for Sessions to resign. He criticized the attorney general for keeping "secret" his conversations with Russian Ambassador Sergey Kislyak, even after then-national security adviser Michael Flynn was fired for misleading Vice President Mike Pence about his contacts with the same Kremlin official.

"When Senator Sessions testified under oath that 'I did not have communications with the Russians,' his statement was demonstrably false, yet he let it stand for weeks," Cummings remarked in a statement. "Attorney General Sessions should resign immediately, and there is no longer any question that we need a truly independent commission to investigate this issue."

In a statement following the report, Sessions denied he had met with "any Russian officials to discuss issues of the campaign. I have no idea what this allegation is about. It is false," he said.

Republicans were more cautious in their remarks, but there were signs that they could step up calls for an outside investigation of the Trump team's ties to Russia as a result of the Sessions news. Right now, the probes are being handled by the House and Senate Intelligence panels, and the FBI is investigating what the intelligence community's interference in the election to aid Trump, and the Trump's teams possible ties to Kremlin officials.

Sen. Lindsey Graham, R-S.C., said at a CNN town hall Wednesday night that if that if there is any substance to allegations regarding the Trump team and Russia, then Sessions cannot be the person to assess them.

"If there is something there and it goes up the chain of investigation, it is clear to me that Jeff Sessions, who is my dear friend, cannot make that decision about Trump," Graham said, stressing that Sessions' contacts with the Russian ambassador could have been "innocent."

"There may be nothing there," he continued. "But if there's something there that the FBI believes is criminal in nature, then for sure you need a special prosecutor. If that day ever comes, I'll be the first one to say it needs to be somebody other than Jeff."

Said frequent Trump critic John McCain, R-Ariz.: "I think we have to know more about it before we make a judgment."

The growing chorus of Democratic lawmakers calling for Sessions' resignation or recusal marks the most serious demands yet to remove Sessions -- a Trump campaign adviser -- from the chain of command in a probe at the Department of Justice he heads. Previously, Democrats demanded that Sessions to recuse himself from Russia-related proceedings and some lawmakers continued to insist on recusal in the wake of the latest revelations.

WATCH: AG Sessions says, "I have not met with any Russians at any time to discuss any political campaign." https://t.co/OcGWQql7P3 — NBC News (@NBCNews) March 2, 2017

Sen. Elizabeth Warren, D-Mass., -- a leading progressive and Trump antagonist -- repeated calls for a special prosecutor to probe Russian influence in the elections and ties to Trump. She also called on Sessions to resign.

She tweeted: We need a special prosecutor totally independent of the AG. We need a real, bipartisan, transparent Congressional investigation into Russia.

Warren followed with another tweet: And we need Attorney General Jeff Sessions - who should have never been confirmed in the first place - to resign. We need it now.

Sen. Brian Schatz, D-Hawaii, also weighed in on Twitter: I'm thinking Jeff Sessions is not the right person to investigate Jeff Sessions.

Several Democratic lawmakers on Wednesday night questioned whether Sessions had lied under oath when he testified at his confirmation hearing in January that he had not had any communications with Russian officials. Rep. Jared Polis, D-Colo., and Mike Quigley, D-Ill., asked whether the former senator provided false statements in his testimony to lawmakers.

Quigley tweeted: It is unconscionable and unacceptable for a United States attorney general-our nation's top law enforcement official-to lie under oath.