* Shelling in rebel stronghold of Donetsk
* Ukraine forces fight street battles with separatists
* Fighting strangling economy - Ukrainian PM
By Richard Balmforth and Thomas Grove
KIEV/DONETSK, Ukraine, Aug 20 (Reuters) - Heavy shelling hit residential neighbourhoods in Ukraine's rebel stronghold of Donetsk and government forces fought street battles in other towns on Wednesday as they sought to crush a four-month-old separatist rebellion.
The forces of the Western-backed Kiev government are steadily gaining the upper hand over the separatists in Russian-speaking eastern Ukraine and are tightening the noose around the main rebel bastions of Donetsk and Luhansk.
Reuters reporters in Donetsk said mortar bombs had struck Chelyuskintsev Street in the north of the city, a few km (miles) from the frontline of the conflict, shattering the windows of several five-storey apartment buildings and shearing off the branches of trees and downing power lines.
The attack left large craters in the street and a metre-wide hole in the first floor of one of the apartment buildings.
"The Ukrainian army or whoever they are - they're bombing us again. I've lived in the apartment building my entire life and now they want to take everything I have. There is nothing left to lose here in this city," said Nina, 52.
The Donetsk city administration, controlled by the separatists, said nine residents had been killed in shelling on Wednesday. The Ukrainian government denies that its forces are targeting civilian areas.
Another nine people, pro-Ukrainian volunteer fighters supporting Kiev's forces, were killed overnight in separate clashes near Donetsk, Ukrainian officials said.
The government in Kiev and its allies have accused Moscow of orchestrating the separatist rebellion and equipping the rebels with tanks, missiles and other heavy weaponry.
Moscow denies this and accuses Kiev of waging a war against its own people and shelling civilians.
The conflict has plunged relations between Russia and the West to their worst level since the end of the Cold War in 1991.
The United Nations puts the death toll in the conflict at 2,086, including civilians and combatants. That figure has nearly doubled since late July, when Ukrainian forces stepped up their offensive and the fighting spread to major urban areas.
"DUST AND SMOKE"
Another Donetsk resident, Lidia, recounted how shelling had hit the shop where she works.
"I hid behind the counter and closed my eyes. When I opened them everything was dark, full of dust and smoke," she said.
"How can we live like this being bombed by the leaders of our own country?"
Six military trucks rumbled past the wreckage of the house, including one equipped with an anti-tank machine gun and a mobile Grad rocket system. Rebels, wearing green camouflage and sunglasses, looked over the wreckage as they passed.
"They'll pay for this," one rebel said, as rebel convoys sped through parts of the city, running red lights.
Elsewhere in the region, Ukrainian forces fought street battles with rebels in the town of Ilovaisk overnight into Wednesday, Interior Ministry official Anton Gerashchenko said.
The nine Ukrainian volunteer fighters were killed in those clashes.
"The enemy can come up to you from wherever he wants and shoot from an attic, a basement or from a children's nursery," Gerashchenko said.
Separately, health authorities said 34 civilians had been killed as a result of fighting in the 24 hours up to noon Wednesday in the wider Donetsk region.
Authorities in Luhansk, the other big separatist stronghold, also reported artillery fire and heavy automatic fire on Wednesday as government forces kept up their assault on rebel positions there.
Luhansk has been largely cut off for weeks and is without water and regular supplies of electricity which have hit mobile and landline phone connections.
Only vital foodstuffs are on sale while long queues form for bread being distributed from vans.
"The humanitarian crisis is critical. Since there's no electricity, people are now cooking meals outside in their yards on open fires," Oleksander Sabenko, a municipal official, told the Ukrainian news channel 112.ua.
As well as worsening conditions for people on the ground, Ukrainian Prime Minister Arseny Yatseniuk said the fighting was draining the potential of the economy by the day, with attacks damaging mines, power stations, rail lines and bridges.
"Russia is aware that rebuilding the Donbass (the industrial east) will cost not millions but billions of hryvnia," he said. (Writing by Dmitry Zhdannikov and Richard Balmforth; Editing by Gareth Jones)