KIEV, Ukraine — Ukraine’s president vowed Sunday to reassert government control over eastern regions as the army unleashed a counter-offensive against Russian-backed separatist fighters vying for command over the airport in the city of Donetsk.

The separatist stronghold was shaken by intense artillery fire over the weekend as a bitter battle raged for the air terminal and surrounding areas.

Streets in Donetsk, which was home to 1 million people before unrest erupted in the spring, were deserted Sunday and the windows of apartments in the center were rattled by incessant rocket and mortar fire.

The warring sides exchanged rocket fire along several points in the roughly 220-mile front line.

Regional authorities loyal to the government said two children, aged 7 and 16, were killed when a rebel shell hit their home in Vuhlehirsk, 45 miles northeast of Donetsk.

A little farther west, in the rebel-controlled city of Horlivka, two were killed and another 16 injured as a result of rocket attacks, city council secretary Oleg Gurbanov said.

PRESIDENT LEADS RALLY

President Petro Poroshenko told a crowd of several thousand gathered in the center of the capital, Kiev, that Ukraine wouldn’t “give up an inch” of its land to Russian-backed separatists.

Hundreds of people, including Poroshenko, held up signs reading “Je Suis Volnovakha,” referring to the 13 people killed when a passenger bus was shelled in the eastern town of that name. The message was an echo of the “Je Suis Charlie” tribute adopted after the terrorist attacks in Paris.

The separatists upped the ante last week by successfully taking over large sections of Donetsk airport, where Ukrainian troops remained despite coming under rocket attacks for months on end. Both sides have incurred losses in the close-quarter combat.

The rebels’ progress has sparked a desperate Ukrainian fight-back supported by a hasty reinforcement of troops and heavy arms.

Yuriy Biryukov, an adviser to Poroshenko, said on his Facebook account Sunday that Ukrainian troops had received orders to unleash heavy shelling of known rebel positions.

“Today we will show just how much we can smash their teeth in,” Biryukov wrote from a location near the fighting.

Separatist statements indicate Ukrainian forces may have tried to burst into Donetsk itself, the first such effort since the unrest started in the spring.

The self-declared Donetsk People’s Republic breakaway government said its forces had repelled a Ukrainian advance toward a bridge leading from the airport into the center.

Ukrainian military spokesman Andriy Lysenko said Sunday that 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.

TRUCE FELL APART

A new truce reached 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 last 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, has accused the Ukrainians of weakening the prospects of that cease-fire deal reached in the Belarusian capital, Minsk.

In a sharply worded statement Sunday, the Russian Foreign Ministry called for an urgent cease-fire.

The ministry said Russian President Vladimir Putin sent Poroshenko a message last week about the necessity for both sides to respect the cease-fire and pull heavy artillery back from the line of contact.

Russia was “ready to use its influence on the separatist fighters to convince them to accept this version,” the statement said. Instead, the Ukrainian forces renewed their shelling of Donetsk, the statement said.

A spokesman for the U.N. secretary-general said Ban Ki-moon was “alarmed by the severe escalation of fighting” around the airport and urged an immediate end to hostilities.