The attacks took place across several parts of the frontline in eastern Ukraine, a military spokesman said, including in Lugansk and the airport in Donetsk, where the two sides have this week tried to put ceasefires in place.
The claims could not be independently verified, but an AFP reporter in Donetsk city said there had been heavy fire, including the use of Grad rockets, throughout the night.
A ceasefire agreed at the weekend is due to come into force on Friday in the Lugansk region -- one of two provinces under rebel control -- although local rebel leaders have said they are not happy with the terms.
The attacks come as US Secretary John Kerry and Russian Foreign Minister Sergei Lavrov are due to come face to face at a meeting of OSCE foreign ministers in Basel, Switzerland on today, where Ukriane is set to dominate the agenda.