Foreign Minister Sergei Lavrov presented the five-page text to the 15 Security Council members yesterday as Russian warplanes hit targets in Syria for the first time.
The draft resolution calls on "all states to participate to the extent possible in these efforts and to coordinate their activities with the consent of the states," according to the text.
After presenting the draft resolution, Lavrov said he expected a "comprehensive discussion" over the coming weeks, but did not specify when it could come up for a vote in the Security Council.
The draft text is similar to a statement drafted by Moscow earlier this month that the United States blocked because of the reference to "consent of the states."
President Vladimir Putin used his speech at the UN General Assembly this week to call for a broad coalition against IS jihadists that would include the Syrian army.
But the United States and its allies have ruled out cooperation with Assad's regime, which they accuse of contributing to IS's rise with a brutal war that has left more than 240,000 dead.
The Security Council in February unanimously adopted a resolution banning all trade in antiquities from Syria, and threatened sanctions against anyone buying oil from IS jihadists.
