Deep inside the Arctic Circle, hundreds of kilometres beyond the frontier of human habitation, a solitary red flag with a white cross flies in the freezing winds, its pole hammered into the unyielding rock of Hans Island. Next to it, a plaque tells the world the Vikings have returned.

The tiny island, a hostile wedge of rock poised between the north-west corner of Greenland and Canada's Ellesmere Island, where winter temperatures plummet to 40C below, is normally home to a seal colony and the occasional polar bear.

Now it's on the front line of the race to claim the North Pole, a modern scramble for the Arctic that has pitted tiny Denmark against its Nato ally Canada, with Russia and the United States lurking in the wings.

At stake, in what could be the last great territorial land-grab, is the promise of untold mineral riches that has prompted an increasing number of governments to throw tens of millions of pounds at scientific and military missions in a bid to get ahead.

These days the Vikings do not come in long ships. The Danish navy sent HDMS Vaedderen, a 3500-tonne frigate with a reinforced hull, into the disputed channel that forms the maritime border between Canada and Greenland, the world's largest island and a semi-independent Danish territory, and more importantly, only 804km south of the North Pole.

And the elite Sirius Patrol, a contingent of specially trained Arctic soldiers, completed a hazardous patrol to the north-east shore of Greenland. The success of the Vaedderen and Sirius missions in proving their ability to operate so far north has given Denmark the confidence to stake its claim to the North Pole.

Trine Dahl Jensen, a geologist, is heading the team of scientists tasked with proving that Denmark's northern frontier is a lot further north than anyone expected. She is more aware than most that the Danes' argument is complex and expensive to prove.

What they must resolve, Ms Dahl-Jensen says, is where Greenland's continental socket ends and where the ocean floor begins. Under the North Pole, the 2000km Lomonosov Ridge of mountains runs from north of Greenland to north of Siberia. If high-tech measurements prove Greenland's socket is attached to the ridge, they are in business. "We must be able to argue that it is a natural extension of Greenland."

In the lobby of her offices at the Geological Survey of Greenland and Denmark there is a mechanical reminder of what they are working towards. A giant Foucault's pendulum is tracking the rotation of the Earth around its South and North Pole axis. So far, no nation has secured territorial rights to either but the dawning of 2005 means the clock is ticking. That is the deadline for the Danish parliament to ratify the United Nations Convention on the Law of the Sea.

The 1986 treaty affords coastal countries an economic zone extending 370km from their shores. If the socket is part of Greenland, then the North Pole could be part of Denmark.

The scientific work has to be completed within 10 years from the date that Denmark ratifies the UN convention. Ms Dahl-Jensen and her team have been given $38 million in Government grants for a project said by the Danish ministry of science to have "historic dimensions".

"In any other situation, we would never have received this kind of funding," she says. At her desk in an overheated, cupboard-sized office lined with polar maps on both walls, the Danish scientist with her blonde hair and broad forehead looks a true descendant of her Viking forebears.

Contrary to expectations, the main challenge her group faced on their first expeditions into the Polar Basin, was weather warmer than usual. "We need cold conditions, preferably between 30 to 40 degrees below," the geologist says. "We can't land [helicopters] on the ice if there is too much water on it."

After landing and setting up camp, the team uses sonar equipment and audio waves produced by controlled explosions and air cannons to map the sea bed. Some of the equipment is in place along the northern shores of Greenland.

But there is a greater imperative behind the latest round of grandiose territorial claims than the workings of international law. The Inuit were among the first to notice it and they do not even have words for what they were seeing. Many indigenous languages have no vocabulary for the legions of animals, insects and plants that have advanced north as global warming melts the polar ice and invites forest to creep over the thawed tundra.

An eight-nation report in November revealed that the Arctic was warming twice as fast as the rest of the planet and that the North Pole could be ice-free in summertime by the end of the century. Around the Arctic, salmon are moving up into more northerly waters, hornets are beginning to buzz and barn owls are appearing in regions where indigenous people have never seen a barn. The Arctic report said polar bears were "unlikely to survive as a species" if the ice disappeared and they were left to compete with their better-adapted brown and grizzly cousins.

What is for some an environmental catastrophe might be a great commercial opportunity. Diamond finds in Canada's Nunavut have fired a mining rush and propelled the country into the ranks of a top-three producer. Ottawa is counting on tapping what the Government suspects are major natural gas reserves in the Beaufort Sea, the frigid zone bordering the Yukon and Alaska, where diplomatic swords were crossed with the US when it tried unsuccessfully to auction the area to oil companies last year.

What no one disagrees with is the riches that would come from the thaw creating a north-west passage. The centuries-old bane of Arctic explorers could become a reality thanks to global warming, cutting thousands of miles off the shipping routes between the Atlantic and Pacific oceans, and delivering a windfall to any country able to tax its users.

In August, Canada spent C$4.9 million ($5.7 million) in a show of force, sending hundreds of troops, helicopters, a frigate and an ice-breaker on a training exercise in search of mock satellite debris. Bad weather grounded planes, two soldiers were lost for a night and a fire on an ageing Sea King helicopter exposed the limits of the present force. This year, the Government has approved the launching of the Radarsat II to provide high-resolution surveillance across the Arctic and monitor ships on the surface.

Canada's Defence Minister, Bill Graham, was well aware global warming has added a new urgency to claims in the Arctic. "[It has created] new possibilities and new threats," he told the New York Times.

The Government has allocated C$70 million ($82 million) for its own underwater mapping. One Canadian diplomat says: "To stake a territorial claim, you must be able to demonstrate you can actively patrol and enforce it, if necessary militarily."

Beneath the pack ice are the nuclear submarines of Russia, patrolling the dark water. Moscow has made a failed attempt to stake its own claim to the Lomonosov Ridge, and thereby to the North Pole.

Faced with a common enemy, Canada and Denmark have begun to negotiate to fund a joint programme, which will divide the hefty expenses. Kai Sorensen, the deputy director of the Greenland and Denmark survey, says Denmark and Canada share a common interest in arguing that the natural divide of the North Pole is formed by the Lomonosov Ridge, which creates a natural median line between Canada, Greenland and across the North Pole to Russian territory.

Moscow has based claims on the so-called sector principle. A division along the median line would give Denmark territorial rights to the North Pole in accordance with the UN Convention of the Law of the Sea, but the sector principle would divide the North Pole along sectors formed by longitudes, thus splitting the Pole into several territories.

Torquil Meedon, a senior official at Denmark's ministry of science and technology, said: "Climate changes indicate that ice in the Polar Sea may disappear within 50 to 100 years. That will open up the north-west passage as a new and valuable shipping route. It will also be open to fishing, and the oil and gas reserves which may prove significant. Who knows how valuable the rights to the North Pole could be 100 years from now?"

Ms Dahl-Jensen says there is no solid evidence to suggest the area of 200,000sq km will contain any wealth of natural resources.

The race to claim new territory is, in large part, about regaining long-lost status. "It is all surreal," says Ole Kvaerno, director of the Institute of Strategy and Political Science at the Royal Danish Defence College. "It really strikes me that various nations have begun to make these impossible territorial claims ... What will be the next territorial claim: space?"

With bragging rights to one of the last, unexplored territories at stake not everyone is being rational. Kvaernoe smiles wryly, and shrugs. "The North Pole; it sounds pretty cool, doesn't it?"