"The secretary general is aware of reports that armed militias have regrouped in Donetsk and Luhansk and that the Ukrainian forces are engaging in intensified military activity," Xinhua quoted Ban's spokesman as saying Monday.
"The continuation of a political and diplomatic process towards a definitive cessation of violence and a peaceful resolution of the crisis is critical," the spokesman said.
"The secretary general urges the Ukrainian authorities to exercise maximum restraint and to take every possible step to ensure the protection of civilians in these areas," the spokesman added.
Thousands of pro-Russian militants Sunday gathered in Donetsk after government forces retook some of their main strongholds of Sloviansk and Kramatorsk in eastern Ukraine.
The rebels still hold the regional capitals of Donetsk and Luhansk and other key areas.
As a response to the recapture of the town by the military, the rebels destroyed three bridges Monday that led into the city of Donetsk.