A rescue operation is underway in the Pacific Ocean after a passenger went overboard on a Carnival cruise.

Carnival Cruise Line tells TMZ ... the Carnival Radiance crew is responding to an overboard alert off the coast north of Ensenada, Mexico.

We're told the cruise ship is returning to where there was a potential sighting of a person in the water ... and we obtained video of rescue boats in the water searching for the passenger, plus footage of someone splashing around.

Folks on board tell us the passenger was watching dolphins near the back of the boat when they went overboard. It's unclear how they ended up in the water.

The Carnival Radiance sails from Long Beach, CA to Mexico ... and the ship was on its way back to Long Beach when the passenger went overboard.

The company tells

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