It is still unclear whether the pair plan to hold substantive talks during their visit to Vietnam following days of mixed messages from the Kremlin and the White House.
Relations between Moscow and Washington have plummeted as a US probe has accused Trump 's former campaign aides of secretly meeting Kremlin-connected officials -- a charge Russia denies.
Trump had previously indicated that he hoped to hold talks with his Russian counterpart during his Vietnam visit, to pressure Moscow into supporting his moves to challenge North Korea's nuclear ambitions.
Both leaders are attending the Asia Pacific Economic Cooperation (APEC) forum in the Vietnamese city of Danang.
At a gala dinner on Friday evening they shook hands and posed briefly for a photo with regional leaders dressed in loose-fitting shirts commissioned for the gathering by current APEC hosts Vietnam .
But there had previously been conflicting indications on whether a full face-to-face was on the cards.
Earlier in the day White House Press Secretary Sarah Sanders had ruled out a bilateral meeting, but the Kremlin suggested it would go ahead.
Pressed on the issue later, Russian Foreign Minister Sergei Lavrov swatted away the question.
'I do not know what the rest of his penpushers are saying, I cannot answer that.'
Both Moscow and Trump had previously suggested that talks were likely to take place.
Trump 's relationship with Moscow has haunted the first year of his presidency.
His former campaign chairman Paul Manafort and an associate are under house arrest on charges including conspiracy to launder money, linked to the investigation by special counsel Robert Mueller into allegations that the campaign colluded with Russia.
Russia has denied allegations of interfering in the US election last year that brought Trump to power.
The two last met during a G20 summit earlier this year.