The Washington Post reported Wednesday that Sessions, then a senator, spoke twice with the ambassador and did not disclose it during confirmation hearings.
Officials told the Post that Sessions did not consider the conversations relevant to the lawmakers' questions and did not remember in detail what was discussed.
The Baltimore Democrat also called for an independent commission to investigate the matter.
"It is inconceivable that even after Michael Flynn was fired for concealing his conversations with the Russians that Attorney General Sessions would keep his own conversations secret for several more weeks," Cummings said in a statement. "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 -- and he continued to let it stand even as he watched the President tell the entire nation he didn't know anything about anyone advising his campaign talking to the Russians. Attorney General Sessions should resign immediately, and there is no longer any question that we need a truly independent commission to investigate this issue."