Government troops trying to quell the pro-Russia insurgency in eastern Ukraine have been focusing on encircling Donetsk, the largest city still in rebel hands, and driving the rebels out of the city of Luhansk.
Several neighbourhoods in Donetsk have been hit with artillery fire in the last few days as fighting on the outskirts has intensified.
The Donetsk regional administration quoted the death toll of 34. Earlier, a Ukrainian official said nine troops were killed in overnight fighting in a town near Donetsk as the government battled to gain control of a major railroad and highway.
Andriy Lysenko, spokesman for the Ukrainian National Security Council, said nine soldiers were killed and 22 wounded in fighting in Ilovaysk overnight.
Fighting is continuing in Ilovaysk after more than a day of hostilities although government forces have gained overall control over the town, Mr Lysenko said.