Although the White House had said no official meeting was planned, the two also shook hands at a dinner on Friday evening and again at the start of the main meeting of Asia-Pacific Economic Cooperation (APEC) leaders on Saturday, Reuters reported.
Television pictures showed Putin and Trump talking as they walked to the position where the traditional group photograph was being taken in the resort city of Danang.
The White House said on Friday that no formal meeting was planned because of scheduling conflicts on both sides, though it was possible they would bump into each other. Trump is on the fourth leg of a 12-day tour of Asia.