Fiji closed "an unfortunate chapter" on Friday with a compensation payout to soldiers exposed to radiation during British nuclear tests in the Pacific more than 56 years ago, the prime minister said.

The payments ended decades of campaigning by veterans and their children for recognition of the serious health problems they suffered after more than 70 Fijians were stationed on Kiritimati, then known as Christmas Island, during the 1957 and 1958 tests.

The British government has refused to pay any compensation, but Fiji Prime Minister Voreqe Bainimarama said the Pacific nation could wait no longer.

"We are righting a wrong. We are closing an unfortunate chapter in our history," Bainimarama told a special ceremony recognising the suffering of the veterans.

"We are bringing justice to a brave and proud group of Fijians to whom a great injustice was done.

"Fiji is not prepared to wait for Britain to do the right thing. We owe it to these men to help them now, not wait for the British politicians and bureaucrats."

The 24 survivors who attended the ceremony each received Fiji$9,855 (US$4,788) from a compensation pool of Fiji$2.95 million (US$1.43 million).

Bainimarama said it was known the veterans suffered ailments including leukaemia and other blood disorders.

Fijian personnel, unaware of the mission they were on, were deployed from the then-British colony of Fiji to Kiritimati, now part of the island nation of Kiribati, during the British tests at the height of the cold war.

"We were only told that we will go there to test some weapons, but when we got there we found out that we were brought there to be part of the British test of weapons of mass destruction," Naibuka Naicegulevu, whose job was to clean and repair vehicles on the island, told AFP.

"My two sons, now in their early 30s get sick suddenly and they can be ill for one week, sometimes more, this is all because of the radiation that we were exposed to," the 76-year-old said.

Bainimarama, whose father Inoke Bainimarama led the Fijian mission, said Fiji could no longer afford to wait for Britain to take the lead on compensation.

"The ranks of these survivors are rapidly thinning. Too many men -- our fellow Fijians -- have gone to their graves without justice. Those who remain deserve justice and Fiji as a nation is determined for them to finally get it," he said.

Thousands of British, Australian and New Zealand veterans of the Kiritimati tests and their families have not received any compensation or special recognition.