There's more I want to say, but the first and most important thing--and if it's the only thing you care to hear, that's fine - is: "I'm sorry", Franken said in the email statement.
Politico reported that Dayton was expected to appoint Lt. Governor Tina Smith to the position if Franken resigned.
In a well-coordinated social media attack, 12 of the Senate's 16 Democratic women took to Twitter or Facebook to demand Franken's resignation.
"I have been shocked and disappointed to learn over the last few weeks that a colleague I am fond of personally has engaged in behavior towards women that is unacceptable".
Texas Democrats said Thursday that they won't give back campaign money generated from a fundraiser headlined by disgraced Sen.
The victor of a special election in November 2018 would serve through to the end of Mr Franken's term in January of 2021.
But they had lost patience with the growing tally of allegations and paved the path for Mr Franken's exit.
"Enough is enough", senator Kirsten Gillibrand declared on Wednesday.More news: During Trump inaugural, Flynn greenlighted nuclear project with Russian Federation
Franken thanked fellow Minnesota Senator Amy Klobuchar and his family before concluding, "This has been a tough few weeks, but I am a very lucky man".
"It's clear to me that this has been a deeply harmful, persistent problem and a clear pattern over a long period of time".
Franken - a former comedian who made his name on the popular late-night show "Saturday Night Live" - announced his decision in an emotional yet somewhat defiant address from the floor of the Senate, where dozens of his colleagues had demanded he step down.
Mr Franken said the idea he would claim such conduct as a right was "preposterous".
The first allegation against Franken - for which he has apologized - was made by sports broadcaster and former model Leeann Tweeden, who said he forcibly kissed her, and touched her without consent as she slept, during a 2006 tour entertaining USA troops deployed in Afghanistan.
Other allegations followed, including a woman who claims Mr Franken put his hand on her buttocks as they posed for a photo at the Minnesota State Fair in 2010.
Various Democratic candidates that can compete in an open primary for the seat.
An Army veteran told CNN later that Franken groped her on a USO tour as well before he was a senator.