Earlier in the day, the Al Jazeera television channel reported, citing UN Special Envoy for Syria Staffan de Mistura, that the talks would take place on March 14.
"The meeting will take place on March 14 and 15," the source said.
The Astana talks on Syrian crisis settlement brought together the representatives of the Syrian government and the armed opposition groups for the first time in the six years of the Syrian war.
As a result of the talks, Russia, Iran and Turkey agreed to establish a trilateral mechanism to monitor the ceasefire that came into effect on December 30, 2016.