Pro-Russian separatists said shelling killed eight residents and wounded 33 more around their stronghold Donetsk.
Across the lines, a local Ukrainian official said six civilians died in five frontline towns in government-held territory and a further 12 were injured.
Ukraine's military said that five of its soldiers were killed and 29 wounded as its forces came under artillery bombardment 93 times over the past day.
The latest casualties come as fighting has surged around east Ukraine in recent weeks, claiming the lives of hundreds of civilians.
Monitors from the Organization for Security and Cooperation in Europe have called for a three-day ceasefire around the beleaguered town to allow the evacuation of civilians caught in the crossfire.
Overall 5,358 people have been killed in fighting in east Ukraine since April, according the United Nations.