The Akademik Fedorov research vessel carrying two mini-submarines to dive 4,200 meters (14,000 feet) below the Pole is trailing a nuclear icebreaker and is set to reach its destination at between 4 and 8 p.m. Moscow time (1-4 p.m. GMT), Russia's Arctic Institute said.
"Favorable weather conditions are expected in the area: weak winds and visibility of up to 20 kilometers [12 miles]," the institute said.
The first-ever dive below the Pole is set to gather scientific data and is seen as a publicity stunt designed to prop up Russia's claim to 1.2 million sq kilometers (about 460,000 sq miles) of the territory - the underwater Lomonosov and Mendeleyev Ridges - which Russia says is the continuation of its continental shelf.
The United States' geological survey data suggest the Arctic seabed contains up to 25% of the world's oil and natural gas reserves, and other mineral riches.
Researchers in the mini-submarines Mir 1 and Mir 2 will take soil and fauna samples on the ocean bed, leave a Russian flag and a message to future generations in a capsule, and establish a video link with the International Space Station.
"It is an extremely important act for Russia, and will demonstrate our capabilities in the Arctic. It is like hoisting a flag on the Moon," a spokesman for the St. Petersburg-based Arctic research institute said earlier.
Russia's veteran explorer and lawmaker Artur Chilingarov, who will be in one of the mini-subs, said earlier the Mirs were capable of working at depths down to 6,000 meters (20,000 feet), but had only been tested at 2,000 meters (6,500 feet). He also said retrieving the vessels was an equally tricky task.
Rivalry over the ownership of hydrocarbons under the North Pole is gaining momentum as the Arctic icecap thins, and oil and gas reserves elsewhere in the world decline.
In mid-July, British endurance swimmer Lewis Gordon Pugh highlighted the drastic changes in the region being brought about by man-made global warming, by swimming 1 km to the Pole, a feat that would have been impossible a few decades ago.
A U.S. State Department senior legal adviser, John Bellinger, told a newspaper on Tuesday that Washington would ratify the UN Convention on the Law of the Sea in order to join a commission to examine Russia and other states' claims to Arctic waters, and has meanwhile closely followed developments in the region.
Under international law, the five countries with territory inside the Arctic Circle - Russia, the U.S., Canada, Norway, and Denmark, which controls Greenland - can claim only a 320-km (200-mile) economic zone around their coastlines.