Steven Seagal, the American actor whose career peaked in the 1990s with movies like “Under Siege” and whose specialty was portraying action figures who spoke softly but blew up buildings and assassinated bad guys, has taken on a new role off screen: that of a Russian citizen with the passport to prove it.

President Vladimir V. Putin personally handed over the actor’s new Russian passport on Friday in a scene at the Kremlin that was considerably more muted than those in Mr. Seagal’s movies. The actor sat across a table from the Russian leader in Moscow, his arms folded or, at times, his hands clasped in a gesture of thanks.

After the Russian leader presented him with the document, Mr. Seagal signed it, according to the Russian news agency TASS and other news outlets.

Mr. Putin told Mr. Seagal, according to TASS, that the two would not “politicize” the event. But the Russian leader, who has said he hoped for better ties with the United States after the election of Donald J. Trump, was also quoted as telling Mr. Seagal: “I would like to congratulate you, and I also hope that this small step will mark the beginning of the gradual improvement in our interstate relations.”

Mr. Seagal replied in Russian, “Thank you very much,” according to TASS.

Mr. Seagal, who is 64 and was born in Michigan, follows in the footsteps of another Western actor whose fame crested decades ago but who managed to emerge in the embrace of Russia: Gerard Depardieu, the French actor, was given Russian citizenship in 2013 after renouncing his native citizenship in a protest over high taxes.

The American boxer Roy Jones Jr. also became a Russian citizen in 2015, The Associated Press reported.

The Kremlin announced on Nov. 3 that Mr. Seagal had received Russian citizenship, but it was not immediately clear why he sought that status. On Twitter, Mr. Seagal has said that he has family ties to Russia but that he never intended to give up his American citizenship.

Mr. Seagal, whose movies are popular in Russia, has defended his forays into that country over the years, especially during times when relations between Washington and Moscow were frosty. (Relations have been severely strained since Russia’s annexation of Crimea, with the United States leading the charge, with European allies, to impose sanctions. With the election of Mr. Trump, Mr. Putin has telegraphed his hopes for better ties.)

The actor has been criticized for his seemingly warm relationship with Mr. Putin. In 2014, he said on his website that he had been misquoted in reports about his opinions on Mr. Putin, saying he had never called him the “world’s greatest leader,” but rather “ONE of the World’s Great Leaders.”

Mr. Seagal’s foray into Russia calls to mind other American celebrities who have drawn attention for their visits to countries whose ties with the United States, if they exist at all, have been exceedingly cold.

Dennis Rodman, the former professional basketball star, has made a series of bizarre trips to North Korea, even as that country detained and paraded American visitors in a geopolitical spectacle. In January 2014, Mr. Rodman even took part in birthday celebrations for Kim Jong-un, the North Korean leader, who is said to be a fan of basketball.

Mr. Putin, for his part, is a fan of the kind of martial-arts movies that Mr. Seagal has executed in his Hollywood career, Reuters reported. The actor first burst onto the national stage with “Above the Law” in 1988.

In 1991, a New York Times review of Mr. Seagal’s movie careerdescribed him as the reigning action-movie star of the time, a “guy with a scowl, a ponytail and an attitude” whose first three films had worldwide box-office and video receipts totaling more than $200 million. Later, he emerged as a Tibetan Buddhist master.