At least 10 people, none of them reportedly children, were killed when shelling hit a school playground in the eastern Ukrainian city of Donetsk. (Reuters)

At least 10 people, none of them reportedly children, were killed when shelling hit a school playground in the eastern Ukrainian city of Donetsk. (Reuters)

Fighting intensified in eastern Ukraine on Wednesday despite a fragile cease-fire, as pro-Russian rebels appeared to be close to capturing the strategically important Donetsk airport.

The fighting was some of the worst since a Sept. 5 truce that calmed the conflict but did not end the hostilities, and city authorities said that at least nine civilians died in the day’s battles. Ukraine’s military and separatist forces said the fighting intensified Wednesday, as rebels vowed to seize the airport, which has remained in government hands for almost all of the six-month-long conflict.

If rebels succeed in taking the airport, they will gain an important means to allow supplies to be brought to their war-torn territory as they seek to build a new state in Ukraine’s southeast. The cease-fire hands over effective control of the territory to the rebels without granting them independence. For the Kiev government, losing the airport would be a major symbolic defeat after its forces suffered heavy losses in a battle in late May to keep it under their control.

Donetsk city government officials said Wednesday that residents are contending with an “extremely difficult situation” and that the part of the city closest to the airport came under “massive bombardment.” At least six civilians were killed when a shell hit a minibus, and another shell hit the grounds of a school, shattering windows and killing a biology teacher and two parents on the first day back at school for students in rebel-held territories, authorities said.

The Ukrainian military denied firing at the school or at the bus. It said its forces came under fire at the airport Wednesday from tanks and Grad multiple-rocket launchers.

View Graphic Map: Ukraine rebels make gains during cease-fire

Despite the continued fighting and rising casualty toll, both sides have been reluctant to declare the cease-fire over, and there were no signs Wednesday that they planned to abandon the political terms of the peace deal reached last month in Minsk, Belarus. The terms include prisoner exchanges and more autonomy for the territories under rebel control. A subsequent agreement spells out the pullback of heavy artillery from the front lines on both sides.

Some artillery has been withdrawn even though fighting has continued at key locations, such as the airport. But major provisions of the deal remain unfulfilled, including a requirement that foreign fighters leave the battlefield, a top U.S. diplomat said Wednesday.

“Russian forces/mil[itary] equipment still in Ukraine, border remains unsecured,” U.S. Ambassador to Ukraine Geoffrey Pyatt said on Twitter. “Now time for Russia and separatists they back to implement Minsk.”

The Kremlin has denied sending its troops to Ukrainian territory, although state-run media have said that some Russian soldiers have fought for the rebels while on vacation.

Kiev’s forces suffered major setbacks in late August after tanks and other heavy equipment streamed over the border from Russia to back up the rebels, and there is little appetite in the Ukrainian capital for a full-fledged return to hostilities.

But open battlefield losses in the middle of the cease-fire also increase domestic pressure on President Petro Poroshenko to take a harder stance against the rebels, who, with Russia’s backing, have seized significant stretches of Ukraine’s industrial heartland. National parliamentary elections are scheduled for Oct. 26, and hard-line nationalist parties are doing well in the opinion polls.

Col. Andriy Lysenko, a military spokesman, said at a briefing in Kiev that the Ukrainian military still controlled the airport and that soldiers there were “brilliantly carrying out their duty,” the Associated Press reported.

A local woman cries in front of a damaged school after shelling in the town of Donetsk, eastern Ukraine, Wednesday, Oct. 1, 2014. Rebels in eastern Ukraine appear to be successfully closing in on the government-held airport of Donetsk. (Darko Vojinovic/AP)

But a separatist leader said that rebel forces were in control of 90 percent of the airport and that they would soon take it over completely.

“In two or maximum three days, we will take control of the Donetsk airport,” rebel leader Alexander Zakharchenko told reporters in Donetsk, the Interfax news agency reported.

In Moscow, Russian Foreign Minister Sergei Lavrov called for an international investigation of deaths in eastern Ukraine during the conflict.

“This is a horrible tragedy, and this is obviously a war crime,” he said, alleging that 400 bodies have been discovered in mass graves near Donetsk.

“We expect that the Western capitals will not hush up these facts,” he said.

A Donetsk rebel leader, Andrei Purgin, clarified Wednesday that 400 people had died in the city during the conflict and that rebels had discovered a grave containing the bodies of nine civilians.

The United Nations estimates that more than 3,500 people have died since the conflict began.