Divers were seen plunging into the harbour at Sandhamn – one of the 30,000 islands off Stockholm – while military speedboats were visible from Haro and Runmaro.
On the island of Korso on Sunday night troops were searching for a mysterious man dressed in black with a backpack, who local people reported seeing wading to the shore.
The Swedish navy showed a grainy photograph of the mysterious “foreign vessel” at a press conference late on Sunday, saying it was the third such sighting since Friday.
“This is not ours, it’s a foreign vessel,” Rear Admiral Anders Grenstad told reporters, referring to the picture taken by a “credible source”.
“He saw something that was on the surface and after he took the picture it disappeared again.”
Mr Grenstad rejected speculation that the armed forces were “submarine hunting” and stressed that the mobilisation – one of the biggest, barring purely training exercises, since the Cold War – was an intelligence operation.
“This is not a submarine hunt, using weapons to combat an opponent,” said Grenstad, adding that an area east of the Swedish capital appeared “to be of interest to a foreign power.”
“Later there can be a situation where it becomes a submarine hunt. We’re not there now.”
Moscow denied that its vessels were involved in any military operations. Stockholm is just across the Baltic Sea from a major Russian naval base in Kaliningrad – a port in the Russian enclave between Poland and Lithuania.
“Russian Navy ships and submarines are fulfilling their duties in the world ocean waters in accordance with the plan,” said a spokesman for the Russian defence ministry. “There has been and there are no extraordinary, let alone emergency, situations involving Russian warships.”
But their denial did not convince Swedish and Russian observers, who said all signs pointed to a submarine becoming stranded underwater.
One analyst, author of the Russian Naval Blog, said on Twitter: “Type 636 SSK Novorossiysk was supposed to go to Northern Fleet for two weeks of dive trials in Sep … Did she get lost?”
Others thought it more likely that there was a small submarine which had got into difficulty, and that a larger “mother ship” was being sent to its aid.
The NS Concord, a Liberian-flagged oil tanker, had arrived in the area on October 4 but in recent days was charted as zigzagging across the seas, as if searching for something. The ship belongs to the Russian shipping company Novo Ship, based in Novorossiysk on the Black Sea. The company is in turn part of the state-owned Sovcomflot, one of the world’s largest oil transport companies, whose CEO, Sergei Frank, is a close confident of President Vladimir Putin.
And last night the Professor Logachev, a research vessel, was tracked heading towards Sweden from St Petersburg – with three Dutch warships following it. The Russian vessel turned off its transponder late on Sunday.
“It’s possible that a small submarine has run aground,” said Bruce Jones, from IHS-Jane’s. “They might have been wanting to look under the highly-advanced ships which the Swedes are operating, to steal their technology.
“Or they could have been on a specific military mission – although the Cold War days of dropping people off from submarines are gone.”
Mr Jones said the submarine was likely to be short range and very small, hence the need for a mother ship. It would be “very quiet, very stealthy and with a very low detection signature,” he said.
“The type of sub would only be known at the highest echelons of naval intelligence.”
Joakim von Braun, an intelligence analyst, said he thought it possible that elite soldiers from the submarine could have swum ashore onto an island, and then hidden in the woods while waiting to be picked up.
If the submarine was abandoned, he said, it is equipped with explosives so that a it can be timed to detonate 24 hours later.
Russia has been criticised in recent months for ramping-up its military peacocking. Last month two Russian aircraft entered Swedish airspace, and the Swedish government complained to Moscow, calling the incursion a “serious violation.”
Russian submarines have been embarking on a new campaign of long-range missions, turning up as far away as the coast of California in sorties designed to test Western detection capability, and to see how the governments would react.
It is a tactic which has not been used on this scale since Soviet days.
According to a report published 25 years ago by the Rand think tank, entitled “Stranger than fiction: Soviet submarine operations in Swedish waters,” said that there were an average of 17 to 36 Soviet underwater operations in Swedish waters from 1980.
The most infamous – and only publicly acknowledged – was the 1981 stranding of a Soviet sub carrying nuclear weapons off Sweden’s southeastern coast, causing an 11-day diplomatic standoff before Swedish authorities allowed the submarine to return home.
Henning Mankell, who authored the Wallander crime novels, wrote The Troubled Man about Soviet spying in Swedish seas.
In the book, the Swedish submariner who is also the father-in-law of Wallander’s daughter goes missing, and then his wife goes missing.
“That is the sort of plot that starts everything in this book,” Mr Mankell has said. “And then I tried to tell the story about all the hypocrisy and all the lying concerning the Swedish neutrality during the 1950s and ’60s and even up to today. That is the basic story of this book.”