The two leaders planned to hold a full-fledged meeting in Buenos Aires at the G20 summit, but on the eve of the event Trump announced its cancellation via Twitter over the recent incident with Ukraine's vessels in the Kerch Strait.
The discussion came after US President Mr Trump scrapped a scheduled meeting with Mr Putin due to Russia's confrontation with Ukrainian ships.
"As long as they remain in power, the war will continue", the Russian leader said.
In remarks to the summit relayed by the Xinhua news agency, Xi reaffirmed his pledges of economic reform "with increased efforts in intellectual property rights protection and more imports".
Russia put on a fearless face after Trump abruptly junked a much-awaited sit-down with Putin, blaming it on internal US politics and "anti-Russian hysteria".
"We had an opportunity to discuss the ongoing process in Northern Syria with the U.S.as two strategic partners".
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Huckabee Sanders did not disclose the content of their conversation, but in a press conference later Saturday Putin revealed that Trump had questioned him about Russia's seizure of Ukrainian ships in the Black Sea.
Germany can't afford being plunged into a war with Russian Federation amid the Kerch Strait crisis, the country's former Vice Chancellor alarmed, blasting Ukraine's suggestion that Berlin deploy its warships to the troubled Azov Sea. Putin told them that the issue of the sailors was a matter for the courts, his spokesman said.
Earlier, Putin grinned broadly and welcomed Saudi Crown Prince Mohammed bin Salman like a long-lost friend with an enthusiastic hand-shake after the group photo, where Trump looked on sombrely and Xi stood impassively.
Merkel used breakfast with Putin on the sidelines of the G20 summit to voice her "concern" over the tensions in the Kerch Strait off Russian-annexed Crimea. Moscow says Ukrainian navy ships entered Russian waters while trying to cross the strait without prior notice, ignoring orders to stop.
"Our talks regarding TurkStream are of great importance", Erdoğan said after the meeting with Putin.
"The President wanted to send a clear, unambiguous message that we find that type of behaviour unacceptable, and so he cancelled the meeting. he wanted to send an unambiguous message that the Russians needed to change that act", he said.