The Kremlin said that during his phone call with Trump, Putin had stressed the "need to keep Syria's sovereignty, independence and territorial integrity intact."
He told Trump that Damascus is in favour of conducting parliamentary and presidential polls.
A political settlement in Syria should be based on principles to be worked out during an all-inclusive "internal negotiating process in Syria," the Kremlin added.
The fate of Assad remains a huge stumbling block, preventing global players from reaching a peace settlement over Syria's six-year war.
At the Black Sea resort of Sochi on Monday, Putin hosted Assad for a surprise summit at which the Syrian leader thanked the Kremlin strongman for his military support.
The talks came ahead of a summit between Putin and the leaders of Turkey and Iran on Wednesday aimed at rebooting the Syrian peace process.
In his phone call with Trump, Putin had also stressed the importance of cooperation between the two countries' security services, the Kremlin said, adding Trump had supported the idea.
The two leaders also discussed North Korea, Afghanistan and Iran.
"Both sides expressed satisfaction with the talks which were business-like and substantial," the Kremlin said.
Trump and Putin met briefly on the sidelines of a regional summit in Vietnam earlier this month but there were no formal sit-down negotiations between the two.
"Vladimir Putin informed Donald Trump of the main results of a meeting with Bashar al-Assad that took place on November 20 at which the Syrian leader confirmed his commitment to the political process, (and) conducting constitutional reform and presidential and parliamentary elections," the Kremlin said.
