Rescue services in New Caledonia were Thursday searching for the body of a fisherman believed to have been killed by a shark, following a spate of fatal attacks in the South Pacific territory this year.

The alarm was raised on Wednesday after fishermen told emergency services they had seen a shark attack a fisherman diving off a beach on the Nouville peninsula northwest of the capital Noumea.

"Our boat is still there but nothing has been found and no one has yet gone to the police or the gendarmerie to report a disappearance," Alexandre Rossignol, head of communications for civil defence, told AFP.

Witnesses recounted the attack to the newspaper Les Nouvelles-Caledoniennes.

"It was very fast. We saw eddies on the surface, it was a shark that was attacking," one witness said. "We saw the fins flapping above the water and then nothing more."

A sea and air search of the area had yet to find the missing fisherman, the local government said.

At least two other people have been killed in shark attacks in the French South Pacific territory of New Caledonia this year
At least two other people have been killed in shark attacks in the French South Pacific territory of New Caledonia this year AFP / Theo Rouby

Swimming and other water sports and activities have been banned along a coastal strip near the attack until Sunday.

Local authorities have also authorised the hunting of bull and tiger sharks in a radius of one nautical mile around the site of the suspected attack for 72 hours.

Several sharks have already been captured, including a 4.3-metre (14-foot) tiger shark, which will be autopsied.

At least two other people have been killed in shark attacks in the French territory off the northeast coast of Australia this year.

A 53-year-old man was killed while paddle-boarding off a beach in the same area of Nouville in late April while in February a 57-year-old man was killed by a tiger shark near Maitre island, a popular tourist site off the coast of Noumea.

Authorities believe the disappearance of a swimmer and a boater earlier this year could also be due to sharks that have settled along the coasts near Noumea.

Worldwide, there were 13 shark attack fatalities last year, according to the Florida Museum of Natural History's International Shark Attack File, more than the global annual average of four.