Those talks were part of an Asia trip in which Trump tried to persuade Russia, China, and other countries to pressure North Korea into giving up its nuclear weapons program.
The Kremlin said Putin also called for co-ordination of anti-terror efforts with the U.S. Afghanistan was also discussed, the Kremlin said.
Syrian President Bashar Assad, arriving in the Black Sea resort of Sochi on Monday, warmly embraced his Russian counterpart Vladimir Putin, nearly resting his head on the Russian president's shoulder.
In a telephone call on Tuesday, Russia's Vladimir Putin and Saudi Arabia's King Salman spoke on the latest efforts on achieving peace in Syria.
Trump and Putin spoke informally several times earlier this month when they attended a summit in Vietnam.
When Assad last visited Russian Federation in October 2015, some observers remarked that Putin appeared cold to the Syrian leader. Putin hosted Assad at a Black Sea resort ahead of a summit later this week with Russia, Turkey and Iran.
The informal talks resulted in a joint statement from the USA and Russian Federation in the Syrian conflict that said the two leaders "agreed that there is no military solution to the conflict in Syria", and pledged to work to develop an "ultimate political solution" to the conflict.
After chatting with Russia's leader in Vietnam, Trump made waves by saying he believed Putin was honest in denying any effort to influence the 2016 presidential election.
"I believe that (Putin) feels that he and Russian Federation did not meddle in the election", Trump said at a news conference in Hanoi, Vietnam.