At least 10 people were killed as residential areas near the airport were caught in the crossfire, further undermining a shaky truce that was imposed last month and has been riddled by violations since.
The rebels and government troops have been waging a particularly brutal fight for the airport. As the Ukrainian-held position closest to Donetsk, it has given government forces a convenient position to target the main rebel stronghold and a defeat there would be a major strategic and symbolic loss.
Ukraine's National Security and Defense Council spokesman Andriy Lysenko told journalists in Kiev that the airport was still under control of government troops who were "brilliantly carrying out their duty" and holding ground there.
However, rebel leader Alexander Zakharchenko was quoted by Interfax news agency as saying that the rebels control 90 percent of the airport, which has been the focus of the worst fighting in the region for weeks.
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Civilian and military casualties have continued to rise despite a cease-fire imposed on Sept. 5. A second agreement between Ukraine, Russia, and the rebels was signed on Sept. 20 that required both sides to remove heavy artillery from the front-line to create a buffer zone between Ukraine and rebel positions.
While the second agreement helped enforce the cease-fire in certain parts of the region where Ukraine troops and rebel forces chose to retreat, other areas have been the scene of non-stop fighting since.
The increasingly violent battle for the airport has caught neighborhoods in the north of Donetsk in the crossfire, driving the civilian death toll even higher in a conflict that has claimed at least 3,500 lives since April.