The secretary to the National Security and Defence Council, Oleksander Turchynov, "is near Mariupol, where units of the national guard broke through enemy defenses and went on the offensive", the statement said.
On Saturday, Kiev said rebels appeared to be massing forces for attacks on strategic towns, including Mariupol, which lies on the Sea of Azov between rebel-controlled areas and the Crimean peninsula. Russia annexed Crimea last March.
The city's vulnerability was exposed last month when 30 civilians were killed there and scores injured in intense rocket attacks. Violence has escalated across the region since then as rebels push a new offensive.
Separatist gains against Kiev government forces in eastern Ukraine, particularly a rebel advance on the transport hub of Debaltseve to the northeast of Donetsk, have added impetus to a Franco-German initiative to try to end the crisis.