Sessions' role in the ongoing probe into Trump campaign's alleged communications with Russian Federation has come under increased scrutiny since the testimony of former FBI Director James Comey this week.
He added that the committee "is the most appropriate forum for such matters, as it has been conducting an investigation and has access to relevant, classified information".
In letters Saturday to Senator Richard Shelby, Republican of Alabama, and Representative John Culberson, Republican of Texas, Sessions said he'd concluded that regardless of which committees he appeared before, the questions would inevitably focus on the Russian probe.
Attorney General Jeff Sessions, right, speaks as Homeland Security Secretary John Kelly listens after the pair toured the ports of entry and met with Department of Justice and DHS personnel in El Paso, Texas, Thursday, April 20, 2017.
Trump at first maintained Comey had been fired as a result of discontent among the FBI agents he supervised, but a day later admitted that he fired the FBI chief as a effect of the bureau's investigation of Russian meddling in USA politics.
Comey branded the president a liar and said he believed he was sacked over his handling of the Federal Bureau of Investigation probe into Russian election meddling, allegations that Trump denied on Friday.
Sessions did not specify whether he would testify in an open or closed setting. Instead, he will send Deputy Attorney General Rod Rosenstein to those hearings to discuss budget matters, Sessions wrote in letters to the chairmen of the subcommittees. He had told lawmakers at his January confirmation hearing that he had not met with Russians during the campaign.
Briefing congressional appropriators on the Justice Department's budget is a critical part of the attorney general's job.
At the conclusion of a February 14 meeting in the White House, Comey testified, Trump urged everyone else but Comey to leave the Oval Office, including Sessions.
Mr Sessions recused himself in March from a federal investigation into contacts between Russia and the presidential campaign of Donald Trump after acknowledging that he had met twice previous year with the Russian ambassador to the United States.
Despite Sessions' admitted talks with Kislyak, he has been dogged by questions about possible additional encounters with the ambassador, including at a foreign policy conference more than a year ago at a hotel in Washington.
"We on the Intelligence Committee want to know the answers to those questions, and we have begun to request information from the attorney general to allow us to get to the bottom of that".