The resumption of violence in the 11-week insurgency threatening to splinter the ex-Soviet state came as Washington slapped sanctions on top separatist leaders and warned Russia against sending troops into Ukraine.
And Russia appeared to be ratcheting up tensions further by putting its central forces on "full combat alert" and ordering snap military exercises that will involve some 65,000 troops.
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"Three soldiers were injured -- one seriously -- and equipment damaged," the border guard service said in a statement.
It added that Ukrainian troops had to return fire when the same militia unit mounted a second attack near a different Russian border crossing a few minutes later.
"The border guards opened fire and repelled the attack," the Ukrainian statement said.
A spokesman for Ukraine's "anti-terrorist operation" reported heavy fighting around the rebel stronghold city of Slavyansk while the defence ministry said one of its anti-aircraft bases was attacked by "50 men in camouflage".
Poroshenko declared the week-long unilateral ceasefire yesterday evening while stressing that "does not mean that we will not fight back against aggression toward our troops."
The order and simultaneous peace plan unveiled by the 48-year-old chocolate baron was immediately rejected by several rebel commanders and branded an "ultimatum" by the Russian foreign ministry.
Poroshenko's attempts to resolve the country's worst post-Soviet crisis two weeks into his term have also been complicated by a new deployment of Russian forces along parts of the border where the rebels mount most frequent attacks.
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