US Secretary of State John Kerry said Russia was responsible for the "distraction, deception and destabilization" of events in eastern Ukraine.
Kerry hailed the record of Kiev's interim authorities, asserting they had been abiding by April 17's Geneva accord to wind down tensions in Ukraine.
The US top diplomat accused Moscow of not doing enough to urge pro-Russian rebels occupying buildings in the country to disarm and withdraw.
He was quoted by the BBC as saying that "not a single Russian official has publicly gone on television in Ukraine and called on the separatists to support the Geneva agreement, to support the stand-down, to give up their weapons and get out of the Ukrainian buildings."
Russia, on the other hand, called on Washington to put pressure on Kiev and force it to stop what it calls an "anti-terrorist" operation in regions near the Russian border.
The latest mutual accusations by US and Russia come after Ukraine's army killed pro-Russian separatists in a raid on a rebel-controlled checkpoint leading into the town of Slaviansk.
After Thursday's attack, which left five rebels dead, Putin declared there would be "consequences" of Kiev's actions in the regions of Donetsk and Luhansk.
He said the authorities were committing "a serious crime" against their own people if they had ordered the use of army against the population.
On Wednesday the Russian Foreign Minsiter Sergei Lavrov warned that Moscow could act in Ukraine as it did in Georgia in 2008, when a brief war was fought with Tbilisi.
Russia's envoy to the UN, Vitaly Churkin, added that his country would have "international-legal grounds" to deploy "peacekeepers to Ukraine", as it did in South Ossetia six years ago.
Churkin was quoted by RBC Daily as warning that the Federal Council could also authorize the use of army forces in the crisis-torn regions of Ukraine.
"This possibility is in our hands. But, of course, it would not be desired".
The Kremlin also called fresh military drills along the border with Ukraine to make the balance of forces "more even", as Defense Minister Sergei Shoigu was referring to Ukrainian army presence in Donetsk and Luhansk regions.
In Kiev, Foreign Minister Andriy Deshchytsia replied that Ukrainian forces were ready to fight Russia.
The verbal standoff between Ukraine and the West, on the one hand, and Russia, on the other, is entering a new intensive phase, as the White House published a petition calling for Russia's designation as a "state sponsor of terrorism".
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