Fears over whale numbers across several species in the Arctic may rob Greenland communities of their traditional hunt.
Scientists from the International Whaling Commission, holding its annual meeting in Italy, do not know if there are enough whales to support the hunt.
For years, Greenland has not provided data to help set safe catch limits.
The IWC allows small communities, mainly in the Arctic and the Caribbean, to hunt in what it calls "aboriginal subsistence whaling", for food.
Greenland's allowance is 187 minkes, the smallest of the great whales, which grow to about 10 metres long in maturity, and 19 fin whales.
The fins are second in size only to the blue whale, the largest creature ever to have lived on Earth: an adult fin whale may reach 20 metres and weigh up to 75 tonnes.
'Bits of information'
The most recent estimates of whale numbers around Greenland date back 11 years for the minkes, and 17 years for the fin whales.
Since 1998 the IWC scientific committee has said its information is inadequate and has been seeking the results of aerial surveys of the whales, as well as DNA samples from all animals killed.
"
Greenland's been spending a lot to try to get the information the committee wants - £100,000 last year, the same again this year
"
Ole Samsing, Danish IWC delegation
The UK-based Whale and Dolphin Conservation Society (WDCS) says "bits" of information have come in, including only 301 samples from more than 1,000 whales killed.
Sue Fisher of the WDCS told BBC News Online: "The committee lost patience this year. It's hit a brick wall."
The committee says if it cannot agree a fin whale population estimate in 2005, it will probably recommend cutting or even abolishing the hunt quota.
The UK fisheries minister, Ben Bradshaw, told BBC News Online: "It's appalling we don't have proper population estimates. There's grave concern over Greenland's whaling."
Greenlanders usually kill minkes either with harpoons which explode inside their bodies, or with rifle shots; fin whales are harpooned.
IWC figures for 2003 show the average time minkes caught off West Greenland took to die after they were hit was 14 minutes, with 31 minutes for east coast catches. One minke survived for five hours.
With fin whales, average time to death was 114 minutes, but one whale harpooned in Greenland last year survived for 12 hours before it died
Greenlanders also kill hundreds of smaller whales, belugas, which are white in maturity, and narwhals, which sprout distinctive tusks.
West Greenland narwhal numbers are estimated to have fallen by 2002 to 15% of their 1986 abundance, suggesting they could vanish in 20 years.
'Internal matter'
The IWC believes both species are locally at risk and has urged Greenland to cut its catches.
Ole Samsing, who heads the IWC delegation from Denmark representing Greenland told BBC News Online: "Greenland's been spending a lot to try to get the information the committee wants - £100,000 last year, the same again this year.
"The hunters are operating in rough water, and I don't think the times the whales take to die are long considering the circumstances.
"Narwhals and belugas are an internal matter for Greenland, but of course it's concerned."
His deputy Amalie Jessen, from Greenland, told BBC News Online she refused to comment on the figures because they had been published by a non-governmental organisation.
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