Sen. Al Franken talks with staff in his office on Capitol Hill on March 14. (Melina Mara/The Post)

Sen. Al Franken (D-Minn.) has waded into the murky waters of trying to apologize for inappropriately touching women — while asserting that he didn't intentionally do anything wrong. And yet Franken hasn't denied any of the accusations against him, leaving the door open to the possibility that he is a serial groper.

In one week, reports have surfaced of four women accusing Franken of inappropriately touching them. Three women have said that while he was campaigning or was a sitting senator, he grabbed their buttocks while they posed for photos. (The two most recent accusations came from anonymous women who shared their stories with the HuffPost in a story published Wednesday.)

In response to the past three accusations, Franken has said he didn't remember the specific events, much less his accusers. And in an apology to his constituents on Thanksgiving, he suggested his accusers got it wrong. Here's part of Franken's response:

“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.”

If you're confused by what he's trying to say here, you're not the only one. Franken's attempt at clarifying what happened only raises more questions, the central ones being: Did he grab these women's buttocks or not? If he did, how, exactly, was it unintentional? Were the women mistaken?

Here's more of Franken's muddy attempt at a denial-apology, which he provided to the Pioneer Press and other local media outlets Thursday:

“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.

By contrast, his accusers left no nuance about what happened: Franken's hand clearly grabbed their buttocks, they say, when they were expecting a professional photo with a politician.

Here's Lindsay Menz, who told her story to CNN about posing for a photo with Franken at the Minnesota State Fair in 2010: “He put his hand full-fledged on my rear. It was wrapped tightly around my butt cheek. It wasn't around my waist. It wasn't around my hip or side. It was definitely on my butt.”

One of Franken's anonymous accusers told her 2007 story to the HuffPost: “I saw him and asked if we could take a photo together for my mother, and we stood next to each other ... and down his hand went.”

His second anonymous accuser told the HuffPost that during a 2008 incident with Franken, “I shook his hand, and he put his arm around my waist and held it there. Then he moved it lower and cupped my butt.”

(In both accusations, the HuffPost confirmed that the woman also told the story privately to confidants at the time it happened, which is one way journalists corroborate claims like these. One anonymous accuser said Franken suggested they visit the bathroom together, which Franken denied.)

Minnesotans react after Leeann Tweeden said on Nov. 16 that Sen. Al Franken (D-Minn.) "forcibly kissed" and groped her in 2006. (Bastien Inzaurralde,Tony Rose,Steve Keller/The Washington Post)

Franken also hasn't denied the claims of his first accuser, Los Angeles broadcaster LeeAnn Tweeden, who said he forcibly kissed her during rehearsal for a skit and also touched her chest while she slept during a USO tour in 2006.

After originally calling Tweeden story's into doubt and downplaying the photographic proof as meant to be “funny,” Franken apologized: "[T]he fact that my own actions have given people a good reason to doubt that makes me feel ashamed.” Tweeden said she accepted his apology.

Is it possible that Franken simply doesn't remember these incidents, and that's why he's offering hedged apologies? Sure. But that doesn't clear up the broader question of whether this is a habit of Franken's. His hands have either grabbed women's private body parts multiple times without their consent, or they haven't.

This is not a murky area. And it's especially confusing coming from a politician who has repeatedly criticized men who cast doubt on their accusers.

In this post-Harvey Weinstein era, one allegation (and photo) of sexual misconduct was enough for most Senate Democrats to say the Senate Ethics Committee should investigate Franken. Franken himself eventually said he welcomed the ethics investigation, which could result in censure or  being removed from the Senate.

As Thursday's statement conveys, Franken seems bent on keeping his job. But he still has a lot of explaining to do about why four women say he groped them.