The allegations against Franken began in mid-November when Los Angeles radio anchor Leeann Tweeden accused him of forcibly kissing her during a 2006 USO tour.
Lindsay Menz, 33, of Frisco, Texas, told CNN last month she was groped by Franken in 2010 at the Minnesota State Fair.
The woman, who is not identified in the story, is reportedly a former Democratic congressional aid and was in her 20s when the incident is alleged to have happened. The second-term senator has also said that he has taken thousands of photos with people over the years and that while he doesn't remember specific pictures or campaign events, any inappropriate behavior was unintentional.
A half dozen Senate Democratic women called for Senator Al Franken to resign Tuesday as a sixth woman came forward to charge that the Minnesota Democrat had made an improper advance on her. She said she ducked his lips, but he said to her as she left, "It's my right as an entertainer".
"I'm shocked and appalled by Sen". "It's clear to me that this has been a deeply harmful, persistent problem and a clear patter over a long period of time".
Murray's backing is significant because she's a member of Democratic leadership and is the highest ranking woman in the Senate.
A spokesman for Minority Leader Chuck Schumer, D-N.Y., had no immediate comment.
"It is clear that Al Franken has engaged in a pattern of egregious and unacceptable behavior toward women, and he should resign", said Sen.
"This allegation is categorically not true and the idea that I would claim this as my right as an entertainer is preposterous", he said.
"I look forward to fully cooperating with the ongoing ethics committee investigation", he said in the statement. After that initial account, several other women came forward to say Franken inappropriately touched them. She released a photo with her statement, that appears to show Franken grabbing toward her chest while she slept.
Mr Franken has apologised to his accusers, but disputes some claims.