One of the victims was Vladimir Rybak, Oleksandr Turchynov said.
Rybak, who recently went missing, was a member of the local parliament and belonged to the President's political party.
"The terrorists who basically have taken the entire Donetsk region hostage have crossed the line with torturing and killing Ukrainian patriots," Turchynov said.
Such crimes are committed with the support of Russian forces, he charged.
But a statement from a pro-Russian leader in Slaviansk rejects the President's claim, and highlights that there is a war of perceptions, too.
Vyacheslav Ponomaryov, the de facto mayor of Slaviansk, placed blame for the deaths on far-right Ukrainian nationalist extremists.
A pro-government party official told CNN that Rybak's family identified his body at the morgue Tuesday.
But the competing claims persist.
As the crisis in Ukraine shows no signs of easing, U.S. Vice President Joe Biden promised support for Ukraine and stressed that the United States won't recognize Russia's annexation of Crimea.
"Ukraine is and must remain one country," he said in Kiev on Tuesday at a news conference with Prime Minister Arseniy Yatsenyuk.
"No nation has the right to simply grab land from another nation," Biden said.
"We will never recognize Russia's illegal occupation of Crimea."
Biden called on Russia to "stop supporting men hiding behind masks and unmarked uniforms sowing unrest in eastern Ukraine."
He warned of additional sanctions if such "provocative behavior" does not end.
Ukrainian and U.S. officials say they think Russian special forces are in the region and are behind efforts to seize government buildings and generally promote unrest -- a claim Moscow denies.
As well as voicing solidarity with Kiev, Biden promised financial support, assistance in reducing Ukraine's dependence on Russian energy sources and nonlethal aid for security forces.
"You will not walk this road alone. We will walk it with you," Biden told Yatsenyuk.
As he spoke, the White House announced a $50 million package of assistance to help Ukraine pursue political and economic reform and strengthen its partnership with the United States.
Biden said he also expects an International Monetary Fund package for Ukraine to be finalized imminently.
The backing is likely to sit well with Ukrainian leaders struggling to keep their country afloat amid dire financial problems, the ongoing showdown with Russia over its annexation of Crimea and alleged interference in Ukraine's pro-Russian east.
Tensions remain high as pro-Russian militants show no sign of preparing to leave occupied government buildings in eastern Ukraine despite an international deal agreed to in Geneva, Switzerland, last week.
"As a result of what's going on in Ukraine," the United States is deploying Army paratroopers nearby, Pentagon spokesman Rear Adm. John Kirby said Tuesday.
Four companies of paratroopers based in Italy will be sent to Poland, Lithuania, Latvia and Estonia over the next few months for military exercises, he said.
Medvedev: Russia can export more to China
But one top Russian official said his country shouldn't be ruffled by talk of increased Western sanctions.
Addressing Russia's lower house Tuesday, Prime Minister Dmitry Medvedev said that Russia can shift its economy east, becoming less reliant on the international banking system and selling more oil and gas to China, state media reported.
Medvedev acknowledged that the sanctions, coupled with instability in the global economy and domestic economic issues, are having an impact.
"Our decision has provoked a rough reaction. Crimea became a reason for a political pressure, which is carried out on the account of so-called sanctions," Medvedev said, according to the state-run RIA Novosti news agency.
He said the circumstances should be a foundation for economic reforms.
"We have all of the needed tools to allow us stable development even in these rough conditions," Medvedev said.
Turchynov: Ukrainians want unity
Turchynov, meanwhile, had strong words for Moscow, saying that "Ukrainians are ready to protect their country from military aggression of the Russian Federation."
A majority of Ukrainian citizens "are for a united, democratic Ukraine with greater powers given to the regions," he said, referring to constitutional reforms promised in a bid to calm fears in eastern Ukraine.
Kiev and Western powers have urged Moscow to use its influence to persuade protesters in the east to lay down their arms, leave the buildings they're occupying and accept amnesty in line with last week's deal.
But Turchynov said Tuesday that "unfortunately, the Russian Federation and its terrorist special forces present in Ukraine are demonstratively not going to implement the Geneva agreement."
He cited the seizure of a police station Monday in the eastern city of Kramatorsk by militants who also took the police chief hostage, "thereby negating the agreements reached in Geneva."
Moscow has said that it holds no sway over pro-Russian protesters and militants.
But Kiev and the United States dispute this.
Meanwhile, a statement from the prosecutor general's office in Kiev criticized law enforcement agencies in a number of cities in eastern Ukraine for not resisting pro-Russian protesters as they seized administrative buildings -- even in cases where they outnumbered the militants.
The statement says self-defense groups in these places were established in reaction to the failings of the security forces.
"These defense groups have the right to bear arms and promise to guarantee public order in their respective regions," it said.
Biden also met with Turchynov and lawmakers in parliament, again stressing Washington's desire to stand with the people of Ukraine.
The country faces very daunting problems and "some might say humiliating threats," he said in an apparent reference to Russian interference, but success is within its grasp.
"We want to be your partner and friend, we want to assist," Biden said.
"We are not suggesting we have all the answers. We are suggesting we stand with you in every endeavor you undertake."
Biden also issued a warning to the leaders in Ukraine, urging them to "fight the cancer of corruption that's endemic" in the country and reform the judicial system.
About $11.4 million of the new $50 million aid package is destined to support Ukraine's planned May 25 presidential vote, which Biden suggested could be "the most important election in Ukrainian history."
And as a step toward reducing Ukraine's reliance on Russian gas, U.S. experts are in Kiev "to help Ukraine secure reverse flows of natural gas from its European neighbors," the White House said.
The promise of further economic help comes on top of a $1 billion loan guarantee already signed by the United States.
The White House also announced Tuesday another $8 million in nonlethal military assistance for Ukraine's military and border service.
It is already providing nearly $10 million in nonlethal aid.
Turchynov's government has talked tough but done little to curb pro-Russian activities in the east, possibly afraid that a crackdown could send Russian forces across the border.
At the same time, the occupation of buildings continues in about a dozen towns and cities across eastern Ukraine.
In three towns, pro-Russian protesters and militants have made it clear to CNN they have no intention of moving until the "illegal" government in Kiev also moves out of official buildings.
Moscow also says the government in Kiev, installed after ousted President Viktor Yanukovych fled Ukraine for Russia in February, is illegitimate and backed by far-right extremists.
Yanukovych's ouster followed months of street protests prompted by his decision last November to drop a planned EU trade agreement in favor of closer ties with Moscow.
Russia annexed Ukraine's autonomous Crimea region last month, following a controversial referendum in which most voters were in favor of joining the Russian Federation.
Source: CNN World