The justice department confirmed he met Sergei Kislyak in July and September last year as part of his role on the Senate Armed Services Committee.
Mr Sessions said on Thursday he did not meet “with any Russians at any time to discuss any political campaign”.
Claims of Russian interference in the election have dogged President Trump.
The US intelligence community believes the alleged Russian hacking of Democratic organisations was carried out to help Mr Trump defeat Democrat Hillary Clinton.
Mr Trump’s National Security Adviser, Michael Flynn, was fired last month after he misled the White House about his conversations with Mr Kislyak, allegedly regarding sanctions against Moscow.
The Democrats have reacted with anger at the latest revelations, saying Mr Sessions should resign and at the very least step aside from an FBI probe he is overseeing into the hacking claims.
What is the basis of the latest allegation?
The Washington Post reported that Mr Sessions and Mr Kislyak held a private conversation in Mr Sessions’s office in September and had spoken earlier in the summer at a meeting with several other ambassadors.
Mr Sessions had meetings with more than 25 foreign ambassadors in the course of the year.
But his meetings with Mr Kislyak came while he was a prominent part of Mr Trump’s campaign team – a so-called surrogate – and amid growing reports of Russian meddling in the US election.
What did Mr Sessions say?
During his confirmation hearing on 10 January, Mr Sessions was asked by Democrat Senator Al Franken: “If there is any evidence that anyone affiliated with the Trump campaign communicated with the Russian government, in the course of this campaign, what will you do?”
Mr Sessions responded: “I’m not aware of any of those activities. I have been called a surrogate at a time or two in that campaign and I did not have communications with the Russians. And I’m unable to comment on it.”
In comments to MSNBC’s Morning Joe programe on Thursday, Mr Sessions reiterated: “I have not met with any Russians at any time to discuss any political campaign, and those remarks are unbelievable to me and are false, and I don’t have anything else to say about that.”
Did Mr Sessions mislead the hearing?
Justice department spokeswoman Sarah Isgur Flores said there had been “absolutely nothing misleading about his answer” at the confirmation hearing.
“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,” she said.
Mr Sessions was also backed by the White House, which condemned the “latest attack against the Trump administration by partisan Democrats”.
Democratic House Minority Leader Nancy Pelosi accused Mr Sessions of “lying under oath” and demanded he resign.
The Democrats have already called for Mr Sessions to recuse himself from the FBI investigation into the hacking allegations.
Some Republicans have also expressed concerns, with congressman Jason Chaffetz, who chairs the House of Representatives oversight panel, saying Mr Sessions “should clarify his testimony and recuse himself”.
Mr Sessions on Thursday repeated that he would recuse himself “when it is appropriate”.
What is the new inquiry about?
News of Mr Sessions’s meetings broke just after a congressional committee agreed to an investigation into Russia’s alleged interference.
The House intelligence panel inquiry will scrutinize contacts between Donald Trump’s presidential campaign and Moscow.
The White House denies any improper behavior during the election campaign, and Russia has consistently rejected allegations of interference.
Until now, Republican senators had been reluctant to agree to Democratic Party demands for the inquiry.
Meanwhile, the New York Times reports that in the last days of the Obama administration, some White House officials rushed to “spread information about Russian efforts to undermine the presidential election – and about possible contacts between” Mr Trump’s team and the Russians.
The paper quotes three former US officials as saying they had two aims – to ensure “such meddling” does not happen in future US and European elections and “to leave a clear trail of intelligence for government investigators”.
How the Russia claims have dogged Trump
May 2016: Reports first emerge of hackers targeting the US Democratic Party. Over the next two months, reports suggest US intelligence agencies have traced the breaches to Russian hackers.
July 2016: Jeff Sessions meets Russia’s envoy to the US Sergei Kislyak and several other ambassadors at an event on the sidelines of the Republican National Convention.
August 2016: Paul Manafort, Donald Trump’s campaign manager, quits after an FBI investigation into his alleged ties to Russian interests in Ukraine and the US.
September 2016: Senator Sessions has a private meeting in his office with Mr Kislyak. The justice department says all meetings were linked to his work on the armed services committee.
October 2016: The US intelligence community release a unanimous statement formally accusing Russia of being behind the hacking of the Democratic Party. Mr Trump questions the findings. Over the coming months, more reports on the hacking emerge. The US intelligence agencies, the justice department and four Congressional committees are all currently investigating the allegations.
February 2017: Mike Flynn resigns as Mr Trump’s new national security adviser after it emerges he discussed the potential lifting of sanctions against Russia with Mr Kislyak and then misleading Vice-President Mike Pence about the communication.
Trump Attorney General Jeff Sessions Under Fire Over Russia Meetings. What did Mr Sessions say? What is the new inquiry about? All that information here.