NATO’s military chief said that Russia-backed forces appear to be “preparing, training and equipping” for a potential new offensive in eastern Ukraine, even as European leaders said the conflict there was entering a “political phase.”

U.S. Air Force Gen. Philip Breedlove, the North Atlantic Treaty Organization’s top commander, said Thursday that the separatist forces have been using the relative lull in fighting since a cease-fire was signed in February to regroup.

“These preparations are consistent with the possibility of an offensive,” Gen. Breedlove said at a Pentagon news conference. “And that is what we have seen through several of the previous pauses in eastern Ukraine.”

The Organization for Security and Cooperation in Europe has warned in recent days of an increase in violence, including heavy shelling last weekend outside the port of Mariupol, the largest government-held city in the area. A top European Union official said this week after meeting with Ukrainian leaders that they fear Russia is preparing a broad attack on their country.

French President François Hollande, German Chancellor Angela Merkel, Ukrainian President Petro Poroshenko and Russian President Vladimir Putin—the four leaders who brokered the Feb. 12 peace plan—agreed in a conference call Thursday that ensuring peace is the “absolute priority,” Mr. Hollande’s office said.