Several Republicans and Democrats have called for Sessions to recuse himself from an investigation into Russian interference in the U.S. election following the revelation he talked twice with Russia's ambassador to the United States during the presidential campaign.
The conversations seem to contradict sworn statements Sessions gave to Congress during his confirmation hearings.
Schumer says a special prosecutor is needed to investigate the allegations of Russian interference and also look into whether the investigation has already been compromised by Sessions.
On Thursday, House Democratic leader Nancy Pelosi accused Sessions of "lying under oath" and demanded that he resign.
"The fact that the attorney general, the top cop of our country, lied to the American people is grounds for him to resign," she said at a news conference. Pelosi later added that "[t]he administration clearly can't be trusted to investigate itself."
—CNBC contributed to this report