The women spoke to Huffington Post on condition of anonymity. The women said the events occurred in Minneapolis in 2007 and 2008.
Franken said in a statement, "It's difficult to respond to anonymous accusers, and I don't remember those campaign events."
Last week, Franken was accused of forcibly kissing a woman while rehearsing for a 2006 USO tour. Franken also was photographed with his hands over her breasts as she slept. A second woman came forward, alleging Franken grabbed her buttocks during a photo op at the Minnesota State Fair.
Senate Majority Leader Mitch McConnell has called for an ethics investigation of Franken, which Franken says he supports.
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