Ukraine's president vowed Sunday to reassert control over his country's conflict-shattered eastern regions as fighting there reached a new peak of intensity.

Petro Poroshenko told a crowd of several thousand gathered in central Kiev that Ukraine wouldn't "give up an inch" of its land to Russian-backed separatists.

The separatist stronghold, Donetsk, was shaken by intense outgoing and incoming artillery fire as a bitter battle raged for control over the city's airport. Streets in the city, which was home to 1 million people before unrest erupted in spring, were completely deserted and the windows of apartments in the center rattled from incessant rocket and mortar fire.

Military spokesman Andriy Lysenko said four servicemen were killed in the previous day's clashes. The office of the General Staff said separately that three troops had been killed in the airport alone.

Donetsk municipal authorities under rebel control said in a statement on their website that several locations all across the city came under shelling. The statement said exits out of the city toward the south remain open, while residents have reported the road to the airport is blocked.

A new truce agreed in early December unraveled one week into the new year despite concerted international efforts to forge a lasting settlement. High-level peace talks expected to take place in Kazakhstan on Thursday were postponed indefinitely.

The U.S. has accused separatists of occupying territory beyond the line of contact agreed upon after a much-violated cease-fire deal in September. Russia, which has been unambiguous in its diplomatic support of the separatist stance, accused the Ukrainians of weakening the prospects of that cease-fire deal reached in the Belarusian capital, Minsk.

Speaking to a Moscow radio station, Kremlin spokesman Dmitry Peskov expressed concern over the surge in fighting in Donetsk, calling it a setback for the prospects of a settlement.

In the largest single loss of civilian lives so far this year, 13 people were killed after a bus parked at an army checkpoint near the eastern town of Volnovakha was hit by a shell Tuesday. Ukrainians swiftly accused separatists, who denied responsibility.

A fact-finding team from the Organization for Security and Cooperation in Europe said Friday evening that the shells had been fired from a "north-north-eastern direction." The Ukrainian said that assessment confirmed their suspicions as the area in question is under rebel control. Russia's Foreign Ministry insisted the OSCE report undermined Kiev's claims, but didn't explain how.

Thousands of people assembled Sunday in Kiev's central Independence Square in an open-air commemoration rally for the Volnovakha victims. Poroshenko and other top government officials attended the ceremony.