WASHINGTON (AP) — Democratic Sen. Al Franken issued a Thanksgiving explanation and apology in the wake of four women alleging that he had touched them inappropriately, a message that ended with a promise to regain constituents’ trust and suggested no resignation was being contemplated.

Franken, elected to one of Minnesota’s Senate seats in 2008, faces a Senate ethics investigation for improper conduct. His statement Thursday didn’t admit to groping or other inappropriate touching but acknowledged that some women felt that he had done something offensive during their encounters. Still, the senator apologized.

“I’ve met tens of thousands of people and taken thousands of photographs, often in crowded and chaotic situations,” he wrote. “I’m a warm person; I hug people. I’ve 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. Some women have found my greetings or embraces for a hug or photo inappropriate, and I respect their feelings about that.”

He continued: “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.”

The multiple accusations against Franken came as the issue of sexual harassment gripped the nation and brought about firings and admonishments against powerful men in politics, entertainment, media and other institutions.

Los Angeles radio anchor Leeann Tweeden said last week that Franken had put his tongue in her mouth during a 2006 USO tour undertaken when the former “Saturday Night Live” writer and performer was still working as a comedian. She posted a photo of Franken with his hands above her chest as she slept wearing a flak vest aboard a military plane. Soon after the post, he apologized to her.

Another woman, Lindsay Menz, said Monday that Franken had squeezed her buttocks in 2010 while posing for a photo at the Minnesota State Fair. Franken said he didn’t remember the picture but expressed remorse that Menz felt “disrespected.” Two more women alleged in a Huffington Post story published Wednesday that Franken touched their buttocks during campaign events in 2007 and 2008.

Franken has not appeared in public since the first allegation, canceling an event in Atlanta for his book “Al Franken, Master of the Senate” and, according to aides, “spending time with his family and doing a lot of reflecting.”