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 United States troops deployed in Afghanistan.
"I may be resigning my seat, but I am not giving up my voice", Mr Franken said in the otherwise-hushed Senate chamber. "I am confident he will make the right decision".
Franken's departure is a headache for Democrats, exposing another seat in a midterm election that already had them defending two dozen incumbents.
Franken said that in responding to women's reports of his behavior, he "wanted to be respectful" of the broader conversation around harassment and men's abuses of power. He says some of the allegations against him are false, while others he "remembers differently". Among them were the top three ranking senators in the party - Minority Leader Chuck Schumer of New York, Dick Durbin of IL and Patty Murray of Washington. She said she was gathering her belongings to follow her boss out of the room. I think that was the right thing to do. The only requirements are that it is a Minnesota resident, at least 30 years old, and a US citizen for at least nine years.
Woods finishes strong with final-round 68 at Hero
Tiger Woods looks to end the 2017 Hero World Challenge on a positive note after a bumpy 75 in Round 3. Whatever I did right ended up in a bad spot, and whatever I did wrong was really wrong.
In a twist of timing, Franken took the floor of the Senate just after departing Alabama Sen. Luther Strange's farewell.
The unexpected opportunity could be a "total game-changer in terms of control of the Senate", Republican strategist Alex Conant, a Minnesota native, told NBC News. The victor of that election will serve until 2020, when he or she would decide whether to run again for a new six-year term.
Starting in mid-November, amid a national firestorm around the issue of sexual assault and harassment, women began to come forward with stories of Franken kissing and groping them without their consent: among them a fellow comedian, a service member Franken met on a USO comedy tour, Democratic volunteers, a congressional staffer, and a former elected official. Even the possibility of a vacant U.S. Senate seat had political operatives scrambling to compile research on the large and growing number of potential candidates.
Dayton's appointment could give someone a running start for a 2018 campaign, but the governor may also choose to simply make a short-term replacement, tabbing someone who doesn't plan to face voters. Dayton said he will announce his choice within days.