"Immediate confidence building measures to strengthen the ceasefire regime, humanitarian access, demining, release of arbitrarily detained people etc." are on the agenda at the moment, the source said.
Russian delegation, headed by special presidential envoy for Syria Alexander Lavrentyev, is holding bilateral meetings with the delegations of the United Nations, Syrian government, Iran and Turkey throughout Tuesday.
Damascus delegation is headed by Syria's Envoy to the United Nations Bashar Jaafari, Iran is represented by Deputy Foreign Minister for Arab and African Affairs Hossein Jaberi Ansari, while Turkey is represented by Foreign Ministry Deputy Undersecretary Sedat Onal.
Syrian armed opposition has so far refused to attend the new meeting on Syria in the Kazakh capital.
The Russian delegation to the Astana talks on Syria is still hopeful that representatives of the Syrian armed opposition may decide to come to the event, the source added.
"There is still some work with them going on. Maybe they will come tomorrow, from Syria's north or south," the source said, asked whether there was a clear understanding on the armed opposition's attendance of this round of talks.