The leaders agreed there was no military solution to Syria's civil war and called on all parties to take part in a Geneva-led political process, according to the Kremlin.
The White House did not immediately respond to questions about Moscow's announcement or the conversation the Kremlin said took place on the sidelines of the Asia-Pacific Economic Cooperation (APEC) summit in the Vietnamese resort of Danang.
The US had earlier frustrated Moscow by stalling on and ultimately rebuffing proposals for a formal talks between the two presidents. The Kremlin had been confident a second bilateral meeting - following their first in July - would take place while the leaders were in Vietnam.
Mr Trump initially said he saw "no reasons" why the talks should not take place, but the White House later rowed back, citing "scheduling conflicts on both sides".
The two leaders did cross paths, however, exchanging handshakes and brief comment during the summit's official dinner.
Pictures showed Mr Trump walking up to Mr Putin as he sat at the summit table and patting him on the back. The two leaned in to speak to each other and clasped each other briefly as they exchanged words.
Television footage from Danang later showed Mr Putin and Mr Trump chatting - apparently amicably - as they walked to the position where the traditional APEC summit photo was being taken at a viewpoint looking over the South China Sea.
In their joint statement, the leaders pledged their commitment to Syria's sovereignty, independence and territorial integrity and called on all parties tin the Syrian conflict to take an active part in a political process.
Moscow and Washington agreed there was no military solution to the Syrian conflict, according to the text of the statement published on the Kremlin's website.
Despite emphasising last year on the campaign trail that he hoped the US and Russia could work together on world issues, Mr Trump has had limited contact with Mr Putin since taking office.
Their brief meeting in Vietnam came amid an intensifying probe into Russian meddling in last year's US presidential election and allegations that the Trump campaign colluded with Moscow.
Mr Trump's former campaign manager, Paul Manafort, has been indicted in the investigation along with his former deputy, Rick Gates, and former foreign policy adviser George Papadopoulos, who has admitted lying to the FBI.
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