In separate statements released almost simultaneously on Wednesday, a group of Democratic lawmakers said the embattled Minnesota senator must step down.
Mr Franken, a former Saturday Night Live comedian, has been accused of groping and sexually harassing seven women, including a US military veteran.
Mr Franken has apologised to his accusers, but disputes some claims.
Senators Kamala Harris, Claire McCaskill, Maggie Hassan, Mazie Hirono, Patty Murray, Kirsten Gillibrand – all prominent female Democratic lawmakers – released their statements online following a US media report that he allegedly attempted to forcibly kiss a former congressional aide in 2006. He denied the claim.