Sen. Lindsey Graham, a South Carolina Republican and another member of the Judiciary Committee, said both Sessions and former Attorney General Loretta Lynch should appear.
Sessions, whose contacts with Russia's ambassador to the US during the presidential campaign has sparked questions, agreed Saturday, June 10, to appear before the Senate intelligence committee as it investigates alleged Russian meddling in the election.
During almost three hours of testimony last week, Comey cryptically told the Senate Intelligence Committee that the Federal Bureau of Investigation had "additional facts" about Sessions he could "not discuss in an open setting".
Comey also has said Sessions did not respond when he complained he didn't "want to get time alone with the president again".
Sessions' testimony is expected to occur Tuesday in a closed meeting and to focus on the moments leading up to the private February 14 conversation where, according to Comey, President Trump pressed the then-FBI director to drop the investigation into former national security adviser Michael Flynn.
Despite his recusal, Sessions in May signed a letter to Trump recommending he remove Comey, the man overseeing the investigation into Russian election meddling and the possible Russia-Trump nexus.
Though the Justice Department maintains that it has fully disclosed the extent of Sessions' foreign contacts previous year, lawmakers have continued to press him for answers about an April 2016 event at the Mayflower Hotel in Washington, where both Sessions and Kislyak attended a foreign policy speech by Trump.
The Senate Appropriations Committee had called in the attorney general to testify about budget issues.
Sessions said Saturday that he was accepting an invitation from the Senate intelligence committee, although that was not immediately confirmed.
Jeff Sessions to appear before Senate intelligence committee
"The Senate intelligence committee is the most appropriate forum for such matters, as it has been conducting an investigation and has access to relevant, classified information", he added.
"This is going to prompt a lot of questions for him", the panel's top Democrat, Senator Patrick Leahy, told AFP of an appearance in which lawmakers will be eager to learn what role Sessions played in Comey's firing last month.
"If, as the president said, I was sacked because of the Russian Federation investigation, why was the attorney-general involved in that chain?"
Senate Democratic leader Charles Schumer of NY said on CBS' Face the Nation he would take Trump up on his offer to testify under oath about his conversations with Comey, inviting the president to testify before the Senate. The following day, Sessions recused himself from the Russian Federation probe, and several top Democrats, including House Minority Leader Nancy Pelosi, demanded he resign.
"In light of reports regarding Mr. Comey's recent testimony", the attorney general wrote in a letter Sen.
Trump's alleged comments to Comey about Flynn "is a big deal, and can't be excused by simply being a novice", Preet Bharara said on ABC's This Week, the first televised interview since his own firing by Trump in March as a federal prosecutor in NY.
Sessions failed to include information about his meetings with Kislyak during his confirmation process.
"There remain a number of questions about his own interactions with the Russians", Republican Senator Susan Collins told CNN Friday.