Kevin Hart Apologizes to Wife, Kids for 'Failed Extortion Attempt' Over Sexually Suggestive Video (UPDATE)

6:39 PM PT -- Sources who have seen the video tell TMZ there are several clips. The first appears to show a woman and Kevin in a club getting cozy. The tape then cuts to a bed, where you don't see the people in the bed ... but hear creaking and what could be people having sex. You never see Kevin in the 2nd clip. The 3rd clip shows 2 people milling around a room, one of them looks vaguely like Kevin.

We're told the person allegedly extorting Kevin has demanded payment from him to avoid the tape's release.

Kevin Hart is getting out in front of a messy situation by apologizing publicly to his wife and kids, and TMZ has learned it's all over a video that looks like he's cheating.

Kevin profusely apologized to his pregnant wife, Eniko Parrish, and his kids on Instagram Saturday ... saying he recently made some mistakes he deeply regrets.

Sources tell TMZ a woman has allegedly demanded money from Kevin after shooting a video with him in which Kevin and the woman are engaged in "sexually suggestive" conduct. We are told it is NOT a sex tape, but looks like it is a prelude to sex. We're told that at a point in the tape when the action is the heaviest, you cannot actually see Kevin.