Updated at 1:53 p.m. ET

Sen. Al Franken said Monday he would not resign from office after allegations of sexual harassment have been leveled against him.

"I know that I've let a lot of people down," Franken said, noting that he was looking forward to getting back to work. "My colleagues, my staff, my supporters and everyone who has counted on me to be a champion for women. To all of you, I just want to again say I am sorry. I know there are no magic words I can say to regain your trust."

He said the process will take time and "that starts with going back to work today."

The Minnesota Democrat spoke to reporters on Capitol Hill for the first time since multiple women have accused him of inappropriate sexual conduct, ranging from forcible kissing to unwanted touching. He took a few questions, reiterated that he would not resign and expressed remorse and regret.

"I've been trying to take responsibility by apologizing," Franken said. He added, "I'm going to be accountable" and "cooperate completely with the ethics investigation."

Franken's conduct has been referred to the Senate Ethics Committee. The committee could recommend anywhere from a reprimand to censure to expulsion, but the full Senate would have to act on that.

Leeanne Tweeden, a radio host in Los Angeles and former model, toured with Franken as part of the USO. She recalled Franken forcibly kissing her during sketches and rehearsals. A photo taken aboard a cargo plane also shows Franken touching Tweeden's breasts over a flak jacket while she was asleep. Looking over his shoulder, Franken smirks at the camera.

Franken said he didn't remember his time with Tweeden the same way, but noted, "I feel that you have to respect women's experience. I apologized to her, and I meant it. And I was very grateful that she accepted it."

Women have also accused Franken of touching their buttocks while taking photos in Minnesota. Franken said he does not remember specific instances in which that happened, but he did not deny that it did.

"One is too many," Franken said. He added that it was disrespectful and he is sorry he hurt them.

"I am tremendously sorry. I am going to have to be much more conscious, much more careful, much more sensitive that this will not happen again going forward. It's going to take a lot more time for me to earn people's trust."

He repeated later, "I am tremendously sorry. ... I am embarrassed. I feel ashamed."

Franken's comments echo what he told Minnesota Public Radio News in an interview over the weekend: "I'm going to go forward. I'm going to take responsibility. I'm going to be held accountable, and I'm going to try to be productive in the way I speak about this."

Democrats have been aiming for the moral high ground on sexual harassment, especially ahead of a Dec. 12 Senate special election in Alabama. Republican Roy Moore there has been accused of sexual misconduct and assault against teenage girls 40 years ago.

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