The White House warned Russia on Friday that Moscow would face tougher sanctions if it failed to abide by a new international deal on Ukraine or moved to send Russian forces into eastern Ukraine.

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"Those costs and sanctions could include targeting very significant sectors of the Russian economy," Susan Rice, President Barack Obama's national security adviser, told reporters.

She said Washington was watching very closely to see whether Russia met its obligations to use its influence to get pro-Russian separatists in eastern Ukraine to disarm and abandon public buildings they had seized.

The agreement, brokered by the United States, Russia, Ukraine and the European Union in Geneva on Thursday, seemed to be the best hope of defusing a stand-off in Ukraine that has dragged East-West relations to their lowest level since the Cold War.

In response, the Kremlin on Friday described the U.S. threat as unacceptable, accusing the White House of treating Moscow like a "guilty schoolboy".

"Statements like those made at a high level in Washington that the United States will follow in detail how Russia fulfils its obligations ... are unlikely to help dialogue," President Vladimir Putin's spokesman, Dmitry Peskov, said.

"You can't treat Russia like a guilty schoolboy who has to put a cross on a piece of paper to show he has done his homework," Peskov said in an interview with Russia's First Channel. "That kind of language is unacceptable."

Also on Friday, separatists in eastern Ukraine said they were not bound by the agreement between Ukraine and Russia, and refused the leave the government buildings. Denis Pushilin, a chairman of the self-appointed Donetsk People's Republic, told reporters that the insurgents do not recognize the Ukrainian government as legitimate, and that though they find the new agreement "reasonable," they would not vacate the government buildings they occupy until the Kiev government does the same.