Fighting has raged on the western outskirts of Donetsk as the advancing Ukrainian army tried to seize control of the rebel stronghold.

The separatists, who are in danger of being encircled, have renewed their calls for Russia to send troops to their aid.

To support their operations, the pro-Russia fighters have been confiscating vehicles and food from residents and businesses in Donetsk. The centre of the major industrial city is all but deserted, with few people or cars on the streets and most stores and restaurants closed.

A spokesman for the Ukrainian military operation, Alexei Dmitrashkovsky, told Associated Press that government soldiers were fighting on Sunday to hold positions they had taken on the edge of Donetsk, but were meeting resistance.

In the part of the city closest to the fighting, an artillery shell hit a school overnight, but no one was reported hurt.

"The shell went through the roof and exploded inside the building, setting off a fire, but we still don't know who fired it," said Dmitry Levonchik, a 45-year-old coal miner. "Who needs this war? What are they fighting for?"

The sounds of gunfire and explosions were heard to the west.

Pavel Gubarev, the self-proclaimed governor of the separatist Donetsk region, said the rebels would win quickly if Russia sent troops.

"Of course it would be great to see Russian peacekeepers here: strong artillery units, tank brigades," Gubarev said. "This war would be over in a day, maybe two."

Ukraine and western leaders say they have evidence that Russia is arming the separatists. Russia denies this and describes the Russian citizens fighting in eastern Ukraine as volunteers.

The ongoing battles had delayed the start of an international search for body parts still lying in the fields where Malaysia Airlines flight MH17 was shot down on 17 July, killing all 298 people on board.

Dutch and Australian experts were able to begin their search on Friday. Early on Sunday, the remains and personal belongings they had found so far were delivered in refrigerated trucks to the city of Kharkiv. The recovered remains will be checked there before being flown to the Netherlands.

Pieter-Jaap Aalbersberg, the head of the recovery mission, said in a statement late on Saturday that the entire area around a chicken farm near the village of Hrabove had been searched and the experts would move to other sites where aircraft wreckage was found. He previously estimated the search would take at least three weeks.