Under international law, five states have territory inside the Arctic Circle - Canada, Norway, Russia, the United States and Denmark, via its control of Greenland.
Moscow's attempt to claim a larger area of the Arctic Circle extending as far as the pole is based on its contention that the Arctic seabed and Siberia are linked by one continental shelf.
"Then Russia can give foundation to its claim to more than a million square kilometres of the oceanic shelf," said a newsreader for Russia's state news channel Vesti-24.
Expedition team members on board a support vessel between the ice sheets of the Arctic celebrated at the news that the mission had been a success.
"There is yellowish gravel down here. No creatures of the deep are visible," said Chilingarov, a veteran Arctic explorer and parliament deputy for the pro-Kremlin party.
Oceanographers in the expedition team will study the seabed and establish that Russia and the North Pole are part of the same shelf.
Sergei Lavrov, foreign minister, said: "The aim of this expedition is not to stake Russia's claim, but to show that our shelf reaches to the North Pole."
Expedition leaders say their main concern is to resurface at the area where they dived. The mini-submersibles are not strong enough to break through the North Pole's icecap.
The Mir-1 submersible reached the seabed at 12:08pm Moscow time (08:08 GMT).
Soviet and US nuclear submarines have often travelled under the polar icecap, but no craft has so far reached the seabed under the pole.
The Arctic seabed is thought to contain resources of natural gas, said Chris Weafer, chief strategist at Alfa Bank in Moscow.
"The exploration that has taken place in the Arctic over the past 15 years, made possible because of the receding icecap, has given very positive indications of substantial structures, particularly natural gas structures," Weafer said.