Analysis by Chris Cillizza, CNN Editor-at-large

(CNN) -- On Monday afternoon, Minnesota Sen. Al Franken apologized.

"I know that I've let a lot of people down, people of Minnesota, my colleagues, my staff, my supporters, and everyone who has counted on me to be a champion for women," he said. "To all of you, I just want to again say that I am sorry."

Broadly speaking, Franken was apologizing for his alleged conduct toward women in a handful of incidents over the past decade. In one, Leeann Tweeden, who was on a USO tour with Franken in the Middle East in 2006, said he kissed her aggressively and fondled her breasts while she was asleep. (Tweeden released a photograph in which Franken appears to be doing just that.) In two other episodes, Franken allegedly grabbed the buttocks of women while taking pictures with them.

What Franken -- after more than a week of refusing to speak publicly about the accusations -- tried to do on Monday was buy himself some time -- both with his constituents and with his colleagues. With Congress back in session after a week-long break, Franken knew he would be confronted by reporters with questions about his conduct. As importantly, he knew his colleagues would face those same questions about him. And he wanted -- and really needed -- to give them something to say, some response that might quiet persistent questions about whether he should resign.

That's why Franken held the press conference. But the problem is that he didn't actually say much of anything.

Yes, he apologized. Or at least he said the words, "I am sorry."

What was way less clear was what, specifically, Franken was apologizing for -- since he reiterated that he simply didn't remember or remembered differently the incidents at the heart of this controversy.

On Tweeden, here's what Franken said:

"Leann and I were on the USO tour together. On the kiss at the rehearsal, we were rehearsing for a sketch. I said that I recall that differently from Leann. But I feel that you have to respect women's experience. I apologized to her and I meant it."

So what, exactly, is Franken apologizing for? Because if Franken remembers the entire episode differently -- and presumably more innocuously -- than Tweeden does, does he really think he needs to say sorry?

On the pictures in which he is alleged to have grabbed women's bottoms, Franken made clear that he doesn't remember these two incidents. Here's what he said Monday:

"I take a lot of pictures in Minnesota. Thousands of pictures. Tens of thousands of people. Those are instances that I don't remember. It has, from these stories, been clear that there are some women -- and one is too many -- who feel that I have done something disrespectful or that hurt them. For that, I am tremendously sorry."

Again, Franken is sorry. But he says he simply has no recollection of touching women inappropriately in a picture. Pressed on how he couldn't remember whether or not he had in an interview Sunday with a local Minnesota TV affiliate, Franken responded: "I can't say that it hasn't happened. In crowded, chaotic situations, I can't say that I have not done that. I am very sorry if these women experienced that."

He has no recollection of doing what he is alleged to have done. But he says he can't say it didn't happen. I say again: So what, exactly, is Franken apologizing for?

Make no mistake: Franken knows he is fighting for his political life here. And he's following a tried and true playbook: Apologize and say you are getting back to work to win back people's trust. Then hope like hell things blow over or some other scandal or controversy knocks you from the front of people's minds.

It might work. But Franken's apologies -- today and over the past week - are undercut by the fact that he either doesn't acknowledge or doesn't remember the conduct he is apologizing for. Which is confusing -- to say the least.