The violence flared several days after a top rebel leader announced a plan to form a new "state" that Kiev warned could put a long-stalled peace plan further in jeopardy.
Ukrainian military spokesman Andriy Lysenko said rebel shelling killed six servicemen and wounded two more around the insurgents' de-facto capital Donetsk over the previous 24 hours.
Three more soldiers were killed and three injured when their vehicle drove on a mine northwest of the second biggest rebel city Lugansk, Lysenko announced.
Donetsk rebel chief Alexander Zakharchenko on Tuesday announced plans to create a new "state" to replace Ukraine.
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The proposed country was to be called Malorossiya (Little Russia) - a tsarist-era term for an area covering much of modern day Ukraine - and have its capital in Donetsk.
The plan appears to be dead in the water after other rebel bosses rejected it and the insurgents' backers in the Kremlin dubbed it a "private initiative."
However, it sparked fears it could drive another nail into the coffin of a stalled peace process that has failed to end a conflict that has claimed 10,000 lives.
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