WELLINGTON, New Zealand (AP) _ An Australian navy ship rescued 12 crewmen from a South Korean trawler that sank off New Zealand, but gave up the search today for three missing crew members.

The trawler, the Dong Chang No. 3, sank Sunday about 60 miles north of Wellington near the Western entrance of Cook Strait.

The Jarvis, a Royal Australian Navy training and support ship, rescued the 12 crewmen from a life raft, then searched for 17 hours in heavy seas for three crewmen who disappeared without life jackets.

Maj. Peter Fry, spokesman for New Zealand's Defense Department, said the missing crewmen's chances for survival ''were assessed as nil after 17 hours in the water.'' There was no immediate word on what caused the trawler to sink.