Syrian President Bashar al-Assad has previously said he has "high hopes" for increased engagement between the United States and Russian Federation to fight ISIS. He said the negotiations should start with discussion of the transition.
The latest diplomacy effort was launched with Russian and Turkish support after regime forces, helped by the Russian air force and Iranian-backed Shia jihadists, defeated opposition factions in eastern Aleppo in December - their biggest setback of the war.
This was the second meeting between the two diplomats before the talks.
During the meeting with representatives of both delegations in attendance, the two sides exchanged views on the latest developments on Astana talks process and the agenda for the second round of the worldwide meeting aimed at finding a political solution for the Syrian crisis.
The Astana initiative has left the West on the sidelines of the latest push to end the war in Syria that has claimed more than 300,000 lives since 2011.
The Syrian government should realize that the Geneva talks will not be "about procedures but about the future of Syria", de Mistura added.
Despite the ceasefire, Muslit said Assad and his allies were "still carrying out crimes" and he accused them of preparing a major assault against the rebel-held Ghouta region to the east of Damascus.
He was referring to the Geneva communique of 2012 calling for the establishment of a transitional governing body with full executive powers that could include members of the present government, the opposition, and other groups.
A new round of talks on Syria conflict led by Russia, Turkey and Iran is taking place in Kazak capital, Astana on Wednesday.
Rebels will send the same delegation to Thursday's talks, headed by Mohammad Alloush of the Islam Army rebel group.