The subs reached a depth of 1.3km (0.8 miles) at a point 87km north of the Franz Josef Land archipelago.
The dives were a trial run ahead of a planned descent later this week to leave the Russian flag on the seabed 4km below the North Pole.
The team is looking for geological evidence to support Moscow's claim to the resource-rich Arctic seabed.
The expedition is being led by two members of parliament - Arthur Chilingarov, a seasoned polar explorer, and fellow MP Vladimir Gruzdev.
"We face the most severe and risky task, to descend to the depths, to the seabed, in the harshest of oceans, where no one has been before and to stand in the centre of the ocean on our own feet," Mr Chilingarov said.
"Humanity has long dreamt of this."
The subs are being launched from the Akademik Fyodorov research ship, supported by a nuclear-powered icebreaker.
"It was the first time a submersible worked under the icecap and it proved they can do this," said the pilot of one of the subs, Anatoly Sagalevich, after the test dives.
Thinning ice in the Arctic has raised hopes of accessing energy reserves.
Russia's claim to a vast swathe of territory in the Arctic, thought to contain oil, gas and mineral reserves, has been challenged by other powers, including the US.
Moscow argued before a UN commission in 2001 that waters off its northern coast were in fact an extension of its maritime territory.
The claim was based on the argument that an underwater feature, known as the Lomonosov Ridge, was an extension of its continental territory. The UN has yet to rule upon the claim.
The teams aboard the mini-submarines Mir 1 and Mir 2 are expected to carry out scientific experiments and measurements on the seabed.
The Law of the Sea Convention allows states an economic zone of 200 nautical miles, which can sometimes be expanded.
To extend the zone, a state has to prove that the structure of the continental shelf is similar to the geological structure within its territory.
At the moment, nobody's shelf extends up to the North Pole, so there is an international area around the Pole administered by the International Seabed Authority.
© 2007 BBC News