Kiev: Ukraine's president vowed today 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 outgoing and incoming artillery fire over the weekend as a bitter battle rages for the air terminal and surrounding areas.

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

The warring sides exchanged rocket fire along several points in the roughly 350-kilometer 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, a town 75 kilometers northeast of Donetsk.

A little further 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 in a statement.

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.

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 armory.

Yuriy Biryukov, an adviser to Poroshenko, said on his Facebook account today 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 attempted 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 today 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.