Some of these moves are rooted in Russia's deep misgivings about western-sponsored regime change in countries such as Libya and Iraq. "They are now getting involved themselves in order to keep the west from making more mistakes," a European diplomat in Moscow says half-jokingly. "We like it, because we need them."
Simultaneously, Moscow has jumped in to build ties with leading countries in Asia, the fastest-growing region: apart from its closer relationship with China, Russia is building friendly relations with Vietnam and India, in competition with the US, and wooing populist Philippine leader Rodrigo Duterte. And Mr Putin is using the desire of Japanese prime minister Shinzo Abe to settle the two countries' territorial dispute to pull this most important US ally in Asia into his orbit.
These moves could put Russia in a key position in mediating conflict in areas such as the disputed South China Sea, or tension between China and Japan.
"Russia has its own post-imperial trauma, like many countries in Europe," says Mr Kortunov. "A key priority for the Kremlin is therefore to bring Russia back as an important player."
This return has paid dividends for Mr Putin domestically. Although polls show that many Russians think he is doing a poor job on the economy and are concerned over the direction of the country, a vast majority strongly back his assertive foreign policy.
And yet Russia faces constraints in its push for a return to the global stage. "Although we have seen several straight years of big increases in military expenditure, this has mostly gone into rebuilding capacities that had fallen into disrepair after the collapse of the Soviet Union," says Ivan Timofeev, an assistant professor at MGIMO, the Moscow university where the foreign ministry trains diplomats. "In the long term, a superpower-style foreign policy is therefore absolutely unsustainable for Russia."
For all the talk of a resurgent country, Russian experts are mindful that without strengthening its sluggish economy, Moscow's push will be severely limited in the longer term. "There are examples in history of economically challenged nations making a big expansionist push and you could imagine that for Russia as well," says Mr Timofeev. "But the economic and social fundamentals for a long-running, sustainable rise of the nation are not in place. We are not like China or India, for whom bigger global influence comes naturally with their growing economic clout."
Even as Russia's economy emerges from a two-year-long recession, the government, the central bank and independent economists all say growth will remain anaemic.
Mr Putin has proved a cunning tactician in exploiting opportunities around the world at limited cost to Moscow. Both western diplomats and Russian officials say there is no way Russia could do without the US or other western countries in its engagement abroad.
"They are seeking out opportunities . . . to insert themselves as a power to be reckoned with," says Mr Rumer. "Yet it's their insistence on being at the table and having a vote and a veto that makes it very difficult to move forward."
With that approach, even Russian strategists doubt how much Moscow's urge to play a role in so many locations will benefit the country in the long term. "If the assumption that the liberal international order will collapse is correct, there may be more opportunities for Russia in the ensuing chaos," says Mr Timofeev. But he argues that is not the most likely scenario, as even challengers of the old order like China are copying its structures and institutions.
"If we end up with a reformed rather than a collapsing international order with a focus on development rather than security — then Russia will be marginalised."