Kyiv said two of its fighter jets were shot down over the rebel-held territory in eastern Ukraine on Wednesday, and the missiles that brought them down might have been fired from Russia.

A spokesman for Ukraine's military operations said the planes were shot down near Savur Mogila, not far from where a Malaysian airliner was brought down last week, killing all 298 passengers on board.

Ukraine's Security Council said the military jets were hit at the altitude of 5,200 metres by missiles that, according to preliminary information, were launched from Russia.

Ukraine's military said two of its fighter jets were shot down in eastern Ukraine on Wednesday. Ukrainian forces, pictured here, have clashed with pro-Russian separatists in the region for weeks. (Gleb Garanich/Reuters)

"They were shot down very professionally. The terrorists do not have such professionals," said Andriy Lysenko, the council's spokesman, referring to pro-Russian rebels fighting the government forces in eastern Ukraine.

The rebels said they shot down the plane themselves.

Fierce fighting raged on Wednesday near the rebels' two main centres in Donetsk and nearby Luhansk, where they have been pushed back in recent days by Ukrainian government forces, who have regained control of villages and suburbs around the cities.

Trenches dug up in downtown Donetsk

A train from Luhansk brought many people fleeing the violence to Kyiv early on Wednesday afternoon.

"It's impossible to live there right now. Fights are going on, apartment buildings are being destroyed, people are being killed," said Galina Berezina, an elderly resident of Luhansk. "Why else do you think I'd flee my own home at my age?"

Kyiv said the separatists were leaving their positions on the outskirts of Donetsk on Wednesday and retreating towards the city centre.

Ukrainian troops patrol roads near Kramatorsk, about 100 kilometres north of Donetsk on July 21. (Gleb Garanich/Reuters)

Residents said the rebels, who rose up in April to demand independence from Kyiv in the mainly Russian-speaking east, had dug trenches in downtown Donetsk outside the main university, where they have been living in student dormitories.

"In Donetsk, rebels abandoned their positions en masse and went towards the central part of the city," according to a statement from the headquarters of what Kyiv calls its "anti-terrorist operation".

"It cannot be ruled out that the appearance of such movements could suggest the spread of panic and attempts to leave the place of warfare."

Residents said they had heard shelling during the night and a shell struck a chemical plant in the city, causing a fire.

Rebels said two journalists had been missing in Donetsk since late on Tuesday. The separatist military commander, Igor Strelkov, a Muscovite, issued an order banning media from operating in combat areas.

Local health officials said 432 people had been killed and 1,015 wounded since hostilities began in the Donetsk region. The uprising started when a Ukrainian president sympathetic to Moscow was forced out of office and Russia then annexed the Crimea region.

Both Kyiv and the West accuse Russia of supporting the separatist rebellion, including by providing fighters, arms and financing. Moscow denies the charges.