Once a rising star in the Democratic Party, Franken made the announcement in a speech Thursday on the Senate floor.
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The two-term lawmaker has repeatedly apologized as several women stepped forward to accuse him of sexually inappropriate behavior, from groping to forcibly trying to kiss them.
But a fresh allegation on Wednesday unleashed a torrent of Democratic demands that Franken step aside. Female senators led the chorus.
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Franken is an actor who appeared on "Saturday Night Live" and an author who narrowly won his Senate seat in 2008 after a prolonged vote count. He has been a fierce opponent of the Trump administration.
His political fall has been swift by congressional standards. The first allegation surfaced on Nov. 16.