Iran, North Korea and Ukraine also were on the agenda, the White House said.
Putin told Syrian President Bashar al-Assad that he was planning to call Qatar's leader following their meeting, according to a statement on the Kremlin website.
Russian Federation is to end its military operation in Syria, President Putin has said, after surprise talks with his Syrian counterpart President Assad.
"I think now the most important thing is to launch political processes, and I am pleased to see your readiness to work with everyone desiring peace and solution", the Russian President said.
Akar headed to Russia's Black Sea resort of Sochi to attend a trilateral meeting earlier in the same day. "We really welcome all those who are interested in the political settlement, we are ready to hold dialogue with them", Syria's Assad said.
Putin and Trump most recently met informally on the sidelines of the APEC summit in Vietnam, where the two leaders had a few encounters and handshakes during "family photos". Putin also called for co-ordination of anti-terror efforts with the USA, the Kremlin said, adding that Afghanistan was also discussed.
Turkey and Russian Federation, together with Iran, are the guarantor countries which brokered a cease-fire in Syria in December 2016, which led to the Astana talks that ran parallel to UN-backed discussions in Geneva to find a political solution to war in Syria. If Erdogan decides to proceed with his plans on the military operation in Afrin, it may create an additional trouble- spot in a war-torn Syria and create an influx of refugees.