Other elements of the measure would give a greater role to the Organization for Security and Cooperation in Europe, Vitaly Churkin told reporters.
Russia has asked the fourteen other members of the Security Council to respond by 10 am (local time) Monday. However, it has yet to request that the panel to meet over the matter.
Two previous attempts by Moscow -- caught up in a standoff with the West over the situation in Ukraine -- to get the Council to agree to a text proved unsuccessful.
The Council "should express deep concern about the increasing number of civilian casualties as a result of intensified combat operations," he said.
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He also urged it to "call on the OSCE to facilitate settlement of the conflict by means of its special monitoring mission."
Russia would allow OSCE monitors to be deployed at two border crossing points on its side of the border, he added.
Churkin accused Ukrainian President Petro Poroshenko of using a June 20 peace plan as "a smoke-screen for intensifying operations in the east of the country" against the insurgents.
His comments came as Ukraine's military reported losing 23 servicemen in clashes across the separatist east that threatened to shatter slim Western hopes of a truce in Europe's deadliest conflict in decades.
The defense ministry said the toll included 19 troops who died in a hail of rockets fired from a truck-mounted Grad rocket launcher system -- a type of weapon both Kiev and Washington insist could only have been covertly supplied to the rebels by Russia.