Icelandic whalers have killed their first two fin whales of the season, local media reported on Thursday, a week after the government allowed the controversial practice to resume under stricter conditions.

Two vessels belonging to Hvalur, the only company still hunting whales in Iceland, each harpooned a fin whale on Thursday and were due back in port early Friday with their catches, several media outlets reported, including national broadcaster RUV.

Iceland is one of just three countries that allow commercial whaling, along with Norway and Japan, in the face of fierce criticism from environmentalists and animal rights' defenders.

Iceland temporarily suspended its whale hunt on June 20 for two months after a government-commissioned report concluded the hunt did not comply with the country's Animal Welfare Act.

Monitoring by Iceland's Food and Veterinary Authority on the fin whale hunt, in which explosive harpoons are used, had found that the killing of the animals took too long based on the main objectives of the Animal Welfare Act.

Shocking video clips broadcast by the veterinary authority showed a whale's agony as it was hunted for five hours.

The government said last week the hunt could resume as of September 1, with "detailed and stricter requirements for hunting equipment and hunting methods, as well as increased supervision."

That included the presence of inspectors from the Directorate of Fisheries on board the boats, filming each kill.

Hvalur's boats had been prevented from heading out to sea immediately after the ban was lifted on September 1.

They were first hampered by poor weather, then blocked for several days by two demonstrators who climbed the vessels' masts to protest against the whale hunt.

The country's whaling season traditionally ends in late September or early October.

Annual quotas authorise the killing of 161 fin whales -- the second-longest marine mammal after the blue whale -- and 217 minke whales, one of the smallest species.

Whalers have however struggled to meet those quotas, killing 148 fin whales last year.

Animal protection charity Humane Society International last week called Iceland's resumption of whaling "a devastating and inexplicable decision".