Oleksandr Turchynov said the politician, named as Vladimir Rybak, was found near rebel-held Sloviansk.
“The terrorists who effectively took the whole Donetsk region hostage have now gone too far,” he said.
The move came as US Vice-President Joe Biden was visiting Ukraine.
After meeting Ukrainian leaders in Kiev, Joe Biden called on Russia to “stop talking and start acting” to defuse the Ukraine crisis.
The US and the West accuse Russia of using undercover military to back separatists in eastern Ukraine, where public buildings are occupied in at least nine cities and towns. Russia denies this.
Joe Biden warned Russia that further “provocative behavior” would lead to “greater isolation” and urged Moscow to end its alleged support for pro-Russian militants.
In remarks to Ukrainian parliament, Joe Biden said the US stood with Ukraine’s new leaders against “humiliating threats” – an apparent reference to Russia.
The vice-president called on Moscow to urge the pro-Russian separatists to leave the buildings they are occupying and to abandon checkpoints.
The US is to provide an additional $50 million for political and economic reforms in Ukraine, including $11 million to help run the presidential election due on May 25.
Announcing the decision to resume the military operation Oleksandr Turchynov said in a statement: “I call on the security bodies to resume and carry out successful anti-terrorist measures aimed at defending Ukrainian citizens living in the east of Ukraine against terrorists.”
Vladimir Rybak, whose body was found on Tuesday, was described as a local councilor for the Fatherland party in the nearby town of Horlivka. The other man killed has not yet been publicly identified.
“These crimes are being committed with the full support and connivance of the Russian Federation,” Oleksandr Turchynov said.
The military operation to end the occupation of buildings began on April 16 but was suspended over the Easter period.
Separately, a Ukrainian military surveillance plane was hit by small arms fire over eastern Ukraine, the defense ministry said.
The aircraft, an Antonov AN-30, suffered minor damage over Sloviansk when it was targeted by automatic gunfire, according to the ministry. No-one was hurt and the plane returned safely to Kiev.
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