Anyone who fell into such waters would typically be dead in 10 minutes without special suits or lifejackets, though nearby fishing boats searched frantically in hopes that some may be in a life raft, New Zealand's rescue coordination center said.
"We were fortunate that there were a number of vessels in the general area (where the boat sank), so they were able to provide assistance," said Ross Henderson, a spokesman for the center.
It was unclear why the vessel sank in light winds and a relatively mild 3-foot (1-meter) swell.
Lee Wu-won of Seoul-based Insung Corporation -- which owns the boat -- said a South Korean fishing trawler operating nearby first contacted Insung officials about the sinking early Monday.
Tearful family members of the missing sailors gathered at Insung's office in the southeastern port city of Busan and waited for news on their loved ones.
The brother-in-law of the boat's missing skipper, Yu Young-sup, said the captain had told him he didn't want to work on the trawler any longer in a recent phone call. "I only hope he will return home alive," Kim Sun-su said, according to South Korea's Yonhap news agency.
The search for survivors was scaled down later Monday, and rescuers said it was increasingly unlikely further survivors would be found. Two New Zealand fishing boats were released from the effort, but three Korean vessels searched on, officials said.
The trawler had 42 people on board when it sunk: eight South Koreans, eight Chinese, 11 Indonesians, 11 Vietnamese, three Filipinos and one Russian, South Korea's Foreign Ministry said in a statement.
The confirmed dead included two Indonesians, two South Koreans and one Vietnamese, a ministry official said, speaking on condition of anonymity because of office rules. He said four Chinese sailors were missing while four other Chinese were rescued.
Many fishing vessels ply the remote seas to haul in deep-water fish such as the Patagonian toothfish, also known as Chilean sea bass, to sell to restaurants around the world. With world consumption of seafood increasing, commercial fleets have begun to operate farther offshore to meet demand.
Rescuers considered calling in aircraft from either New Zealand or from the U.S. Antarctic research station on McMurdo Sound, but Henderson said the plan was abandoned because neither plane could reach the distant search area in time to find survivors.