Three crewmen missing from a fishing vessel that docked at Bluff Harbour with a dead body on board have been found.

Detective Sergeant Dave Kennelly said they were found just after 5am today on the southern outskirts of Invercargill in good health.

The three Vietnamese men are in custody under the Immigration Act and the matter has been handed to Immigration New Zealand.

Kennelly said a Chinese national died on the boat and when it docked on Monday the three men fled.

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Kennelly said the man died in the Southern Ocean, within international waters, but New Zealand is the closest country so "we have the obligation to investigate".

Immigration assistant general manager Peter Devoy confirmed the three crew members were unlawfully in New Zealand.

"They are being held in custody under section 313 of the Immigration Act and will be interviewed by INZ compliance officers before any deportation or other action takes place. The injured crew member has been granted a visa for two weeks to receive medical treatment. For legal and privacy reasons INZ is unable to make any further comment."

Kennelly said it wasn't a criminal investigation.