Hawaii’s longline fishing industry could lose the right to fish for tuna in a large swath of ocean south of the islands under new federal rules limiting the number of accidental catches that kill or seriously injure false killer whales.

The industry would be banned from tuna fishing in the southern exclusion zone for the rest of 2013 if there is a second incident this year in which a longline boat causes injuries likely to be fatal to a false killer whale in federal waters around Hawaii.

The first incident happened Jan. 29, when a false killer whale suffered likely fatal injuries from longline fishing in federal waters north of the Hawaiian Islands, the National Marine Fisheries Service said.

“The animal came up and broke the line,” said Nancy C. Young, a federal marine mammal biologist with the agency.

Young said a federal observer on board witnessed the incident.

The southern exclusion zone covers 112,575 nautical square miles and represents about 15 percent of U.S. waters surrounding Hawaii. It is south of the main Hawaiian Islands and within the U.S.

Exclusive Economic Zone with boundaries 200 nautical miles around the main and Northwestern Hawaiian Islands.

Scientists said the southern exclusion zone was selected as a place for the conditional fishing ban because it has a higher concentration of false killer whales than other places.

The longline industry employs about 1,000 people aboard an estimated 130 boats and provides much of the fish in Hawaii’s markets, according to Hawaii longline officials.

Scientists and fishermen said the effect of the new rules are going to be difficult to assess because of the migratory nature of tuna and false killer whales.

Jim Cook, who owns six longline fishing boats, said he’s unsure how a closure of the southern exclusion zone would affect the industry.

The rule limiting fatal or serious fishing-related injuries to false killer whales to two in a calendar year took effect on Dec. 31.

Other federal rules, which took effect on Feb. 27, call for the use of a thinner hook and stronger line to enable the longline industry to catch tuna but allow false killer whales to break free.

Earthjustice staff attorney David Henkin said federal officials took weeks to make a determination about the Jan. 29 injuries to the false killer whale.

“That’s not acceptable,” Henkin said.