The Kremlin has repeatedly denied allegations of interfering in the USA election and Trump denies any collusion between his campaign and Russian officials.
Sessions later said he recalled the meeting following news reports about it.
"The Attorney General of the United States should not be held to a different standard than the young police officer whose life you ruined", Jefferies said.
A day earlier, the Washington Post reported Sessions ordered top prosecutors in the department to look into these areas and report back to him, possibly to make the case for a special prosecutor. "I did not, and I'm not aware of anyone else that did, and I don't believe it happened". "I have always told the truth, and I have answered every question as I understood them and to the best of my recollection, as I will continue to do today". He has "no clear recollection" of the March 2016 meeting where George Papadopoulos offered to set up a meeting between Donald Trump and Vladimir Putin - but the attorney general does remember shooting down the campaign aide's unseemly suggestion.
Sessions said that was the version of events he recalled.
"I have not been improperly influenced and would not be improperly influenced", Mr. Sessions said. Those details complicate Sessions' effort to downplay knowledge of the campaign's foreign contacts. He said he mentioned in passing to Sessions that he was preparing to visit Russian Federation and Sessions "had no reaction whatsoever".
The Congressmen-both of whom site on the Judiciary Committee-published their ultimatum in a Fox News op-ed Monday.
The matter took on new life after a report last month said the FBI was investigating possible Russian attempts to influence the US nuclear sector at the time CFIUS was considering the sale of Uranium One to Rosatom. He told reporters he was "honest and correct" in his response in the hearing, although he acknowledged he should have mentioned he had met with the ambassador in his role as a senator.
Democrats on the House Judiciary Committee pressed Mr. Sessions to explain whether he was pressured to restart investigations targeting President Trump's former democratic rival. "I have made a decision to recuse myself from any existing or future investigations of any matters related in any way to the campaigns for President of the United States", he said.
The hearing was starkly divided.
Sessions has asked Justice Department prosecutors to decide if a special counsel should be appointed to investigate certain Republican concerns, including alleged wrongdoing by the Clinton Foundation and the sale of a uranium company to Russian Federation, according to media reports on Monday.
Sessions was cautious on that score.
Democratic members of the House Judiciary Committee advised Sessions in a letter last week that they meant to press him on what they said were "inconsistencies" between the attorney general's past statements and the new revelations.
Asked in a House Judiciary Committee hearing whether he would review requests for a prosecutor "fairly and expeditiously", Sessions confirmed he would.