BALTIYSK, Russia — Russia held civil defense drills involving 40 million people this month, the largest since the collapse of the Soviet Union. State media broadcast instantly recognizable Soviet imagery, showing schoolchildren trying on gas masks, and urge viewers to find the nearest bomb shelter “before it’s too late.”

But while these reports fuel Western fears of a new Cold War, ordinary Russians don’t seem too worried.

Even in Kaliningrad, a heavily militarized Russian outpost surrounded by NATO members Lithuania and Poland, people see the messages as mere posturing.

The harbor of Baltiysk, home of Russia’s Baltic Fleet, is downright sleepy. On a recent morning, fishermen lounged by the pier as sailors put a fresh coat of paint on a missile ship across the bay.

“It’s laughable because no one here is planning to attack anyone,” said Olga Zyukina, feeding swans with her 16-month-old son. “I think our president is smart and he has no need to give such orders.”

NATO held a high-profile summit in nearby Poland in July, and the Western alliance’s troops are building up positions in Poland, Estonia, Latvia and Lithuania as tensions with Russia escalate. The United States is sending 1,000 troops to Poland next year, and its concerns about an unwanted confrontation with Russia have played heavily into President Barack Obama’s reluctance to engage militarily in Syria’s civil war.

In an interview published Tuesday with the Guardian newspaper, the chief of British spy agency MI5 said Russia is an increasing danger to the West.

“It is using its whole range of state organs and powers to push its foreign policy abroad in increasingly aggressive ways — involving propaganda, espionage, subversion and cyber-attacks,” Andrew Parker said, adding: “It is MI5’s job to get in the way of that.”

Russia, for its part, held a flurry of Baltic Fleet exercises this year, with marines practicing landings, ships firing surface-to-air missiles, fighter jets dropping bombs and troops capturing saboteur divers. Last month, Moscow sent nuclear-capable Iskander missile units to Kaliningrad. With an estimated range of 500 kilometers (300 miles), the missiles could reach the Baltic states, most of Poland and southern Sweden.

Moscow has also upped the bellicose talk. Russian state television presents the NATO exercises as testament to aggressive intentions of the West. News bulletins are filled with rapturous reports about missile testing, and Moscow officials proudly announce that the city’s bomb shelters are ready to accommodate all 12 million residents.

“There will be just a few minutes to find a shelter that can save your life — seven minutes to be exact, which is the travel time of the nearest missiles of a potential adversary,” an NTV reporter said in front of footage of a screaming crowd rushing for shelter.

This adds to a sense of unease as the military exercises heat up. Oleg Skvortsov, a 36-year-old business consultant from Kaliningrad, was celebrating his wife’s birthday across the border in Lithuania, enjoying a sunny day on idyllic pastures with rabbits jumping around.

“And then we heard a thud, and a rocket flew in the direction of Kaliningrad. It turned out our guys had held drills, and Lithuanians decided to have their own,” he said. “It was really scary. It happened once and I don’t want to feel like this all the time.”

Alexei Milovanov, editor in chief of the independent news website NewKaliningrad.Ru, dismisses the military displays as “saber-rattling” but says he understands why Kaliningrad’s Western neighbors are worried.

“If you keep a rifle at home, you know you have it and you can use it if something happens,” he said. “But if you go out on the porch with this rifle every day and parade it in front of everyone, people will start giving you strange looks.”

To be sure, some Russians are fearful of another Cold War — 27 percent, according to a nationwide poll by the independent Levada Center last month. The poll, which interviewed 1,600 people in 48 Russian regions, had a margin of error of 3 percentage points.

“Of course I’m worried,” said Natalya Bezprozvannaya, a 43-year-old cook who lives on Russia’s westernmost tip, a seven-minute ferry ride from Baltiysk. “To be honest, I’m a little bit scared because they talk about it on television.”

But mostly, Kaliningrad residents say their lives go on much as usual.

“You don’t feel it here. It’s all on television,” said Yuri Velikotsky, a retired naval captain who is now an amber craftsman. “I don’t feel that we’re getting prepared for a war. This isn’t the way you get prepared for one. It’s just the usual war of nerves.”