A senior military source in Severomorsk, speaking on condition of anonymity, said the captain Sergei Lappa "called the towing vessel by radio, saying a leak had been found at the propellor joints at the rear of the sub, in compartment nine."
The seamen attempted to seal off the compartment, "but the water continued to pour in," he said.
They also attempted, without success, to release the last reserves of compressed air into compartment eight in order to create an air pocket in the flooded area, he said.
Lappa called his superiors on the towing vessel to suggest allowing the submarine to sink in shallow waters near Kildin island which they were passing.
The submarine was still stable at that moment, the source said. However, the towing vessel's officers turned down the suggestion and ordered the crew to carry on with their efforts while awaiting the arrival of help.
The seamen attempted to seal off the compartment, "but the water continued to pour in."
Senior military source
When compartments eight and nine were both filled with water, the pressure on the attachments between the submarine and the pontoons became too strong, causing the submarine to break away, first to the fore and then aft.
The submarine then foundered within a few minutes, giving little chance for the crew, the source said.
Only one of the 10 crew members survived. The bodies of two others were recovered from the icy waters, and the seven others are still missing, their bodies presumed to be trapped inside the sunken vessel.
Meanwhile, the search operation in the Barents Sea continued on Tuesday, with helicopters examining the waters and nearby coastal areas.
Russian officials said that the submarine's nuclear reactors were shut down and that there was no likelihood of pollution.
Defence Minister, Sergei Ivanov, on Sunday said the accident had been the result of negligence.
The defence ministry earlier said the sinking early on Saturday came after towing pontoons broke away during a heavy storm as it was being towed to port to be scrapped.
The sinking revived memories of the Kursk disaster in the same area three years earlier in which 118 seamen died.