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Chuck Schumer speaks at a press conference on Capitol Hill
Sessions had said during his confirmation hearing for attorney general in January that he "did not have communications with the Russians" while he served as a top adviser and campaign surrogate for Donald Trump.
Rep. Jason Chaffetz, who leads the House Oversight Committee, tweeted on Thursday, "AG Sessions should clarify his testimony and recuse himself." Chaffetz has recently faced criticism from his constituents, who argue the congressman is not investigating the Trump campaign's ties to Russia aggressively enough.
House majority leader Kevin McCarthy said Thursday morning that Sessions' recusal is necessary "to make sure everybody trusts the investigation." The California Republican later walked back the comment.
Other prominent Republicans are defending Sessions.
House Speaker Paul Ryan told reporters that he sees no "purpose or reason" for Sessions to recuse himself unless he becomes the subject of an investigation.
Sen. Ted Cruz called the accusations "political theater," arguing Democrats are "feigning outrage about a perfectly ordinary meeting between a sitting U.S. senator and a foreign ambassador."
Senate Majority Leader Mitch McConnell, Republican of Kentucky, declined on Thursday to comment on the issue. Republican Sen. Chuck Grassley, who chairs the Judiciary Committee which held Sessions' confirmation hearing, has not yet commented on the issue.
Many top Democrats are demanding that Sessions resign, accusing him of lying to Congress and thus perjuring himself.
"Sessions is not fit to serve as the top law enforcement officer of our country and must resign," House Minority leader Nancy Pelosi said in a statement on Thursday.
Senate Minority leader Chuck Schumer said in a press conference on Thursday that Sessions should resign "for the good of the country."
"Attorney General Sessions had weeks to correct the record that he made before the Judiciary Committee, but he let the record stand," Schumer said.
Sens. Bernie Sanders and Elizabeth Warren have both called for Sessions to resign and for a special prosecutor to be appointed to conduct an independent investigation into the Trump campaign's ties to Russia.
Trump told reporters on Thursday that he had "total" confidence in Sessions, although Trump said he "wasn't aware" of Sessions' meeting with the ambassador. When asked whether Sessions spoke truthfully during his confirmation hearing, Trump said "he probably did."
Sessions denied the accusations and slapped away suggestions that he should recuse himself from the investigation or resign from office. He has argued that his comments during his confirmation hearing were meant to apply only to his role as a campaign surrogate and not as a senator.
"I have never met with any Russian officials to discuss issues of the campaign," Sessions said in a statement on Wednesday night. "I have no idea what this allegation is about. It is false."