The airport, on the fringes of the rebel stronghold of Donetsk, has been at the center of bitter battles since May. Control over it was split between the separatists and Ukrainian forces who had held onto the main civilian terminal. Reduced to little more than a shell-littered wreck, the building is of limited strategic importance but has great symbolic value.
An AP reporter saw a rebel flag hoisted over that building Thursday, although fighting still appeared to be ongoing. Ukraine insisted government troops were holding their positions at the airport.
The rebel leader in Donetsk, Alexander Zakharchenko, said the separatist offensive would continue and its goal was to recapture all territory lost to government forces last year.
If the separatists do advance further, that would undermine the chances of resurrecting a September cease-fire that laid out specific demarcation lines between the opposing sides. The rebels' disregard of that agreement appears to defy Moscow's public backing of the peace deal.
The battle for the airport took place as Ukraine held a day of mourning for 13 people killed Tuesday when their bus was hit by what the government says was a rebel shell.
President Petro Poroshenko said respects would be paid for all people killed by rebel offensives.
The separatists deny responsibility for the deaths and accuse Ukrainian forces of staging an attack in a bid to smear them. OSCE observers said the bus showed "damage consistent with a nearby rocket impact."
Ukraine and the West have routinely accused Russia of fomenting unrest in the eastern Ukraine. Moscow denies that accusation, although it admits that Russian citizens, including soldiers, are involved in the fighting in Ukraine.
In Kiev, the Ukrainian parliament on Thursday approved a presidential decree for three waves of military mobilization this year. Poroshenko said that was motivated by the worsening security situation.
Leonard contributed from Kiev, Ukraine.
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