A dispute over an abolished tax rebate for whalers means there will likely be no fin whale hunt off Iceland this year, the head of the only company that catches the giant whales said Wednesday.

Hunters of fin whales -- the second largest whale species after the blue whale -- are demanding that their company, Hvalur, compensate them for losing the tax rebate they used to receive for having to work far from home for long periods, Hvalur chief Kristjan Loftsson said.

"We will never agree to this. If this is how it's going to be there will be no hunting this summer," he told AFP, adding, "We will see about next year."

Loftsson's company, the largest whaling firm in Iceland, caught 148 fin whales in 2010, but none last year due to the disintegration of its only market in quake- and tsunami-hit Japan.

It had planned to catch up to 70 fin whales this year, since the Japanese market "is slowly moving in the right direction and normalising," Loftsson said.

Iceland's hunt for the much smaller minke whales is however continuing as planned, with four whales killed so far out of an annual quota of 259, according to the fisheries ministry.

The International Whaling Commission imposed a global moratorium on whaling in 1986 amid alarm at the declining stock of the marine mammals.

Iceland and Norway are the only two countries still openly practicing commercial whaling in defiance of an international moratorium in place since 1986.

Japan also hunts whales but insists this is only for scientific purposes even if most of the meat ends up on the market for consumption.