"As a result of shelling, Ukraine has lost seven soldiers while 24 were injured," army spokesman Vladyslav Seleznyov said, adding that rebels had fired 115 times.
The governor of the separatist Lugansk region also reported two civilians killed.
Rebels allegedly supported by Russia have pulled out of peace talks and announced a new offensive in eastern Ukraine, raising international concern and prompting calls for Moscow to rein in the insurgents.
Ukraine's military said most of the rebel fire overnight occurred to the northeast in the Lugansk region. Pro-Kiev authorities in both Lugansk and Donetsk said they planned to evacuate children from several areas in the war zone.