The Interfax news agency said Adm. Viktor Fyodorov announced that the rescue vessel also was trying to raise the vessel as it was being towed.
The small submarine became entangled in a fishing net on yesterday and was stranded off Russia's Pacific coast in about 600ft of water.
At that depth, the crew would not be able to swim to the surface and divers likely would be unable to reach them. However, bringing the sub into shallower waters would potentially make it accessible to divers or even allow the crew to escape on their own
Both the Royal Navy and the US Navy had volunteered to send unmanned underwater vehicles to help rescue efforts, at Russia's request. Japan has also volunteered to help.
The Royal Navy's remote-controlled submersible is equipped with cameras and an arm which British officials believe could untangle the submarine. A RAF C-17 transport plane is preparing to fly from RAF Brize Norton to Prestwick Airport, near Glasgow, to collect the vehicle and fly it to Russia.
But the announcement that the mini-submarine was under tow appeared to be the first significant positive sign in a day of desperate drama amid contradictory reports about how quickly the trapped crew's air would run out.
Fyodorov said there was enough air aboard to last until Monday, although other officials had said there was barely more than a day's supply.
The crisis evoked comparisons with the 2000 disaster involving the nuclear submarine Kursk.
The Kursk sank to the bottom of the Barents Sea after explosions on board, killing all 118 seamen aboard. Russian President Vladimir Putin was sharply criticised for his handling of the crisis and an initial reluctance to accept foreign assistance.