Vladimir Putin’s new geopolitical ambitions have led the US to realise it made a strategic mistake turning away from Europe and making a pivot to Asia, the foreign affairs adviser to the Polish president has said.

Krzysztof Szczerski urged the west to recognise that the Russian president was no longer simply seeking to restore his country’s dominance in former Soviet states such as Ukraine, but to adopt a more dominant military posture across the globe.

He told the Guardian: “It is now a strategy of geopolitical confrontation, so the next strikes of Putin are not guaranteed to be in the post-Soviet sphere. It could be anywhere in the world. It is wrong to think that Putin has narrow territorial limits. Syria has shown that is not the case.”

Szczerski said Putin’s Syrian intervention last year showed Russia had the capacity to move large amounts of equipment at speed across a great distance without their preparations being noticed. “His capacity to set these new challenging fronts around the world should be an alarm call,” he said.

Russian fighter jets on the ground in Syria’s Latakia province. Photograph: AFP/Getty Images

Poland is hosting a Nato summit in July and is pressing the alliance to increase its military presence in eastern Europe by stationing two heavy brigades. They would be underpinned by regular joint military drills and become a core part of Nato defence plans.

Szczerski said on Friday that Poland was pleased by the US decision, announced at the beginning of the month by the American defence secretary, Ash Carter, to quadruple its investment in defence equipment to $3.4bn (£2.4bn) in a “European reassurance initiative”.

He said: “This signal of Obama to quadruple the amount of money on the eastern flank is a sign that something has changed the other side of the Atlantic. America, for the first time in a couple of years, is coming back to Europe. They realised that this pivot to Asia was a mistake.”

Poland wants Nato to station the two heavy brigades – typically between 3,000 and 5,000 troops – on Polish soil in response to Russia’s intervention in Ukraine, where Moscow denies it is actively assisting pro-Russian rebels.

Nato has so far been reluctant to station troops permanently in central Europe, with some states wary of violating a 1997 Nato-Russia agreement on the size of forces the alliance can have in former Warsaw pact countries, of which Poland is one.

Szczerski said: “Nato should be present on the eastern flank because Russia on the other side of the border is building its offensive capacity in the region. Their offensive capacities should be matched. It is Russia that is defining the level of security in the region by its acts and by its decisions.

“Nato should come back to its roots so it is an alliance that is guaranteeing the defence security of its own territory in a cohesive way so it should be able to defend every member of our alliance. That means reinforcement and presence.”