Norway and Denmark will be represented by their foreign ministers, Jonas Gahr Store and Per Stig Moller, respectively, and Canada by Natural Resources Minister Gary Lunn. The United States has sent Deputy Secretary of State John Negroponte.
The Foreign Ministry of Denmark, the meeting's host country, said the states are expected to reiterate their willingness to abide by existing rules and treaties, including the 1982 United Nation Convention on the Law of the Sea.
The sides are expected to adopt a joint declaration saying the United Nations will rule on possible territorial disputes.
Russia has claimed ownership of a vast section of neutral arctic territory, believed to be rich in oil and gas.
The meeting in Greenland will also focus on climate change, which scientists have warned could destroy all floating summer ice in the Arctic in the next few years.
"We need to send a common political signal to both our own populations and the rest of the world that the five coastal states will address the opportunities and challenges in a responsible manner," the Danish foreign minister said.
Under the Law of the Sea, coastal states hold sovereignty over a zone of 200 nautical mile (370 km) limit, but this area can be extended if it is a part of the country's continental shelf or shallower waters. Some Arctic shelves extend for hundreds of miles, creating a possibility of overlapping territorial claims.
Last August, as part of a scientific expedition, two Russian mini-subs made a symbolic eight-hour dive beneath the North Pole to bolster the country's claim that the Arctic's Lomonosov Ridge lies in the country's economic zone. A titanium Russian flag was also planted on the seabed. Russia first claimed the territory in 2001, but the UN demanded more evidence.
The expedition irritated a number of Western countries, particularly Canada.
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One of the main achievements of the 6th BRICS Summit was the signing of an official document on establishing a New Development Bank with a declared capital of $100 billion. The creation of the bank is an important step towards institutionalizing BRICS and strengthening its positions in the world in the long run.