The 1982 convention outlines the rights and duties of countries in their use of the oceans, establishing guidelines in a wide range of areas, including the environment.
Harper's Magazine reported in August that the U.S. had been secretly measuring the Arctic seabed since 2003, intending to apply for an expansion of its continental shelf to include the seabed's oil and gas reserves after the Senate ratifies the sea law convention.
Russian Natural Resources Minister Yury Trutnev said on Tuesday that the Russian government had started work to prepare an application to the UN to include in its underwater economic zone the Lomonosov Ridge.
The area is part of the Arctic territory Russia has claimed since 2001, on the grounds that the underwater mountain chain and the Mendeleyev Ridge are a continuation of its continental shelf. In August, two Russian mini-submarines made a symbolic eight-hour dive beneath the North Pole to bolster the country's claim to the territory, planting a titanium flag on the seabed.
The Arctic territory could add 80 million tons of oil and 426 billion cubic meters of gas to Russian reserves, bringing the country an additional 1.35 billion metric tons of oil equivalent.
In 2001, Russia first claimed its right to the territory, but the UN demanded more evidence.
Under international law, the five Arctic Circle countries - the U.S., Canada, Denmark, Norway and Russia - each have a 322-kilometer (200-mile) economic zone in the Arctic Ocean.
A Republican senator from Alaska, Lisa Murkowski, said on Wednesday that if the UN convention is not ratified by the U.S., the U.S. would have to deploy an aircraft carrier strike group in the Arctic Ocean.
She said Alaska is interested in the U.S. becoming a member of the convention in order to both expand its continental shelf in the Arctic and to extract resources.
The White House backs the convention's ratification, as do senior U.S. defense officials and oil and gas industry officials.