The announcement, following talks between UN envoy Geir Pedersen and Foreign Minister Walid Muallem, was the first time that Damascus has spoken of progress towards forming the panel.
“Great progress was made towards reaching an agreement for a committee to discuss the constitution,” the foreign ministry said.
Pederson in a statement on Twitter reported “good progress” and said both sides were “getting closer to reaching an agreement to establish a constitutional committee”.
“Looking forward to discussions w/ the SNC shortly,” he added, referring to the commission representing the country’s opposition.
Pedersen, a seasoned Norwegian diplomat who took over the job in January, arrived in Damascus on Tuesday hoping to push ahead with stalling efforts to end the eight-year civil war.
His predecessor, Staffan de Mistura, stepped down after his four years in the post ended with a year-long abortive push to form the constitutional committee.
The regime wants to amend the existing constitution, while the opposition has called for a new one.
Discussions have been bogged down in disagreements over the composition of the committee, to be made up of 150 members: 50 chosen by the regime, the same number by the opposition, and another 50 selected by the UN envoy.
Pro-government newspaper Al-Watan on Tuesday reported that a body could start work at early as September if Damascus agreed to Pedersen’s list.
Last month, the United States said it was time to scrap the constitutional committee initiative and come up with other ways to end the war.