"We urge the UN Special Envoy for Syria to report back to the Security Council on his progress no later than October 31," the ministers of the group, which includes Egypt, France, Germany, Jordan, Saudi Arabia, the United Kingdom and United States, said in their joint statement.
The ministers said it was "imperative" to make progress toward a political solution in line with UN Security Council Resolution 2254.
The group issued the joint statement after they met on Thursday on the sidelines of the United Nations General Assembly (UNGA) in New York.
De Mistura said earlier this week on the sidelines of the UNGA that launching of the constitutional committee of Syrians is very possible in October.