Sen. Al Franken. (Carolyn Kaster/AP)

Sen. Al Franken (D-Minn.), who has been accused of inappropriate physical contact with several women, apologized Thursday to the people of Minnesota and said he is "committed to regaining their trust."

Franken faced allegations last week that he had physical contact with four women without their permission. He faces a Senate ethics investigation for improper conduct and hasn't been seen publicly since the first claims of misbehavior last week.

On Thursday, the senator issued a Thanksgiving statement of explanation and regret — and a pledge to regain the trust of Minnesotans, suggesting that he wasn't planning on resigning as some have called on him to do.

In the statement provided to the Minneapolis Star Tribune and Minnesota Public Radio, Franken wrote that as a "warm person" he hugs people and that he's learned from recent stories that "in some of those encounters, I crossed a line for some women — and I know that any number is too many."

He added: "Some women have found my greetings or embraces for a hug or photo inappropriate, and I respect their feelings about that. I've thought a lot in recent days about how that could happen, and recognize that I need to be much more careful and sensitive in these situations.

"I feel terribly that I've made some women feel badly and for that I am so sorry, and I want to make sure that never happens again. And let me say again to Minnesotans that I'm sorry for putting them through this and I'm committed to regaining their trust."

Los Angeles radio anchor Leeann Tweeden said last week that Franken had put his tongue in her mouth during a 2006 USO tour, before he became senator. She also posted a photo of him with his hands above her chest as she slept wearing a flak vest aboard a military plane. Franken, 66, has apologized.

Another woman, Lindsay Menz, said Monday that he had squeezed her buttocks in 2010 while posing for a photo at the Minnesota State Fair. Franken, by then a senator, said he didn't remember the picture but expressed remorse that Menz felt "disrespected."

In a story published Wednesday by the HuffPost, two more women alleged that Franken touched their buttocks during campaign events in 2007 and 2008.

Franken canceled a sold-out appearance in Atlanta to promote his book "Al Franken, Giant of the Senate." His aides have said he's "spending time with his family and doing a lot of reflecting."