Six people died in shelling and gunfire on the outskirts of Donetsk and city officials said three were killed in shelling of Luhansk over the previous 24 hours.
In central Donetsk shelling echoed through the night and witnesses said several buildings caught fire in the outlying Petrovsky district, including a school. The smell of smoke stretched as far as the city centre.
Many residents of Luhansk, which is close to the border with Russia, have no electricity and some are without water.
Advances by the Ukrainian army have forced the rebels out of most of the towns they had occupied in Russian-speaking east Ukraine and squeezed them mainly into Luhansk, which had a population of about 400,000 before the conflict, and Donetsk, which had about 1 million residents.
The Ukrainian military said it had suffered no losses in the latest fighting.