Ukraine also made fresh accusations of Moscow backing the separatists, alleging that hundreds of Russian troops crossed the border into rebel-held territory to join the fight.
After a pause in the fighting early today as Orthodox Christians celebrated Epiphany, clashes reignited in the afternoon, with regular explosions heard coming from the direction of the Donetsk airport northwest of the city.
The airport has been the flashpoint of an upsurge in violence in recent days that has left a September truce in tatters, with heavy combat shaking the area at the weekend after Ukraine launched a major counter-offensive to push out the rebels.
A university across from the hospital was also hit and there was speculation in the neighbourhood over whether the intended target was the nearby separatist security ministry.
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Larissa Polyakova, who was nearby, said students at the university barely missed being hit.
"Shells fell on the window," she said. "Miraculously, the students had left the room 15 minutes before. Can you imagine what would have happened if they were still inside?"
Concerns mounted over the fate of civilians, with rebels said to be launching attacks from residential areas and Ukrainian forces accused of returning fire.
"The use of heavily populated areas for launching attacks by pro-Russian separatists in Donetsk and Horlivka and the return of fire into these areas by pro-Kiev forces is putting civilian lives in great danger," Denis Krivosheev, deputy Europe and Central Asia programme director for Amnesty International, said in a statement.
Ukraine's military reported at least three soldiers killed over the last 24 hours and another 66 wounded, but claimed to be in control of the airport.