Russia has helped Assad's forces to take back most of the country but the eight-year-long war continues. Swathes of the northeast and northwest are out of his control, while sanctions and a fuel shortage are constricting the economy.
Moscow has pushed for a political process involving talks on a new constitution and elections as a way to end the conflict, but Assad has played down the possibility that the Turkey-backed opposition or foreign countries might participate.
Russia's Foreign Ministry said late on Friday that Assad had met Moscow's Syria envoy Alexander Lavrentiev, Deputy Russian Foreign Minister Sergei Vershinin and several Russian Defence Ministry officials.
However, while it said they had discussed the formation of a constitutional committee, which Syria's opposition last year agreed to join under U.N. auspices after a Russian-hosted peace conference, Syrian state media did not mention it.
Syria's official SANA news agency said meetings had focused on the next round of talks in Kazakhstan involving Syria, its allies Russia and Iran, and the rebels' backer Turkey.
Hundreds of thousands of people have been killed in Syria's war and about half the pre-conflict population of 22 million has been displaced.
Russia launched a military intervention to support Assad in 2015, turning the tide of the fighting in his favor.
On Saturday, SANA said Assad had met Russian Deputy Prime Minister Yury Borisov to discuss trade and economic cooperation, "particularly in the fields of energy, industry and increasing trade."
It said Assad and Borisov discussed mechanisms to overcome obstacles including those "resulting from the sanctions which countries against the Syrian people imposed on Syria."
The United States and European Union imposed tough sanctions on Syria early in the conflict over what they described as atrocities carried out by the government, which it denies.
This week, Syrian state media reported that a fuel shortage which has resulted in rationing and long queues at petrol stations came in the context of difficulty in importing fuel and the halting of a credit line from Iran.Syrian Foreign Minister Walid al-Mouallem said in a statement on Saturday carried by SANA that "Syria is always coordinating with Iran."