In a phone call with Russian Foreign Minister Sergei Lavrov, US Secretary of State John Kerry expressed "deep concern over the lack of positive Russian steps".
Russia blames Kiev's leaders for the collapse of last week's Geneva accord, BBC reported.
Ukraine's acting president earlier ordered the relaunch of military operations against pro-Russian militants in the east of the country.
It came as President Oleksandr Turchynov said two men - including local politician Vladimir Rybak - had been found dead after being "brutally tortured".
"The terrorists who effectively took the whole Donetsk region hostage have now gone too far," he said.
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 involvement.
In his conversation with Lavrov on Tuesday, Kerry "urged Russia to tone down escalatory rhetoric, engage diplomatically in the east... and issue public statements calling for those occupying buildings to disarm," according to a senior State Department official.
"Secretary Kerry also reiterated that the absence of measurable progress on implementing the Geneva agreement will result in increased sanctions on Russia," the official said.
The warning came after US Vice-President Joe Biden met Ukraine's new leaders in Kiev, and called on Russia to "stop talking and start acting" to defuse the Ukraine crisis.
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