Kiev military spokesman Andriy Lysenko said two government troops were killed and six wounded in mortar fire and shelling across swathes of the eastern separatist Donetsk province over the past day.
Lysenko told reporters that "activity had especially picked up" around the industrial Sea of Azov port of Mariupol that the rebels have been trying to seize to establish an export gateway for the steel and coal mines they now control.
Separatist negotiator Denis Pushilin called the reported attack "a grave violation of the Minsk agreement" that Russia and Ukraine signed in mid-February during talks involving the leaders of Germany and France.
The four countries' foreign ministers are due to meet in Paris on Tuesday to try to salvage the accord.
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June has witnessed an upsurge in violence that has killed more than 50 people after a three-month lull.
Kiev sounded a pessimistic note about the odds of diplomats being able to reverse that trend.
"Either we achieve concrete results, or we demonstrate clearly that Moscow does not want to fulfil the Minsk agreements," he said yesterday.
Ukrainian President Petro Poroshenko will send his personal envoy to Minsk on Tuesday to meet Pushilin and other rebels for their own round of European-mediated talks, after a similar meeting last week ended in deadlock.
"With progress like this, the chances of a complete political settlement of the conflict are in grave doubt," Pushilin said.
The two predominantly Russian-speaking provinces of Lugansk and Donetsk have been waging a war for independence from Kiev's new pro-Western leadership since March 2014.
It has also exposed the Kremlin to Western charges -- repeatedly denied by President Vladimir Putin -- of trying to inflict permanent damage on Russia's ex-Soviet neighbour in retribution for its sudden shift to the West.