Franken became the second prominent Democrat to announce his departure from Congress this week amid sexual misconduct allegations. Rep. John Conyers of Michigan stepped down Tuesday after more than 50 years in Congress after former staffers' accusations of misconduct.
The push for Franken's resignation came as Moore runs for Senate in Alabama amid allegations of sexual misconduct with teenagers when he was in his 30s decades ago.
In his parting speech, Franken lashed out at the GOP for its treatment of accusations against Moore and Trump.
"I, of all people, am aware that there is some irony in the fact that I am leaving while a man who has bragged on tape about his history of sexual assault sits in the Oval Office and a man who has repeatedly preyed on young girls campaigns for the Senate with the full support of his party," Franken said.
White House press secretary Sarah Sanders said: "The president addressed the comments back during the campaign. We feel strongly that the people of this country also addressed that when they elected Donald Trump to be President."
Republican Senate leaders have urged Moore to drop out and said they plan to immediately start an ethics investigation into him if he wins. But the Republican National Committee has resumed giving money to his campaign. Trump formally endorsed Moore in a phone call Monday.
Franken, a former writer and performer on NBC's "Saturday Night Live," is serving his second term in the Senate. The resignation marks a rapid fall for a lawmaker who was widely mentioned as a possible 2020 Democratic presidential candidate only months ago.
Most Senate Democrats called for Franken's resignation on Wednesday. Among them were the top three ranking senators in the party — Minority Leader Chuck Schumer of New York, Dick Durbin of Illinois and Patty Murray of Washington. Democratic National Committee Chairman Tom Perez also tweeted that Franken should step down. In addition, Senate Majority Leader Mitch McConnell called for Franken's resignation.
In the statements, the Democratic senators used words like "egregious" and "unacceptable" to describe Franken's behavior.
On Thursday, the senator called serving in the chamber the "great honor of my life."
"I know in my heart that nothing I have done as a senator, nothing, has brought dishonor on this institution, and I am confident that the ethics committee would agree," Franken said.
The former aide who spoke to Politico in its story published Wednesday said the incident took place after a taping of Franken's radio show, before he was a senator.
"'It's my right as an entertainer,'" the woman says Franken told her after she avoided his kiss.
In response to the claim, Franken said: "This allegation is categorically not true and the idea that I would claim this as my right as an entertainer is preposterous. I look forward to fully cooperating with the ongoing ethics committee investigation."
When Franken steps down, Minnesota Gov. Mark Dayton, a Democrat, will pick a successor who will serve until a special election next year. The winner of that election will serve until 2020, when he or she would decide whether to run again for a new six-year term.
Franken is only the latest in a string of powerful American men who have left their jobs in the wake of sexual harassment or assault allegations. Those include Hollywood producer Harvey Weinstein and newsmen Matt Lauer and Bill O'Reilly.
Time magazine on Wednesday named "The Silence Breakers" — those who have come forward with their stories about being victims of pervasive sexual harassment — as 2017 Person of the Year.
Disclosure: NBC and CNBC are owned by Comcast's NBCUniversal unit.