The US has threatened tougher economic sanctions if Russia fails to abide by a new international agreement to help de-escalate the crisis in Ukraine.
The Kremlin responded by accusing the White House of treating Moscow like a "guilty schoolboy" over the deal.
Meanwhile, Ukraine's foreign minister said "anti-terrorist" operations in the east would be put on hold over Easter.
Pro-Russian separatists in several cities are refusing to leave buildings, defying a key term of the accord.
Russia, Ukraine, the EU and US had agreed during talks in Geneva that illegal military groups in Ukraine must be dissolved, and that those occupying government premises must be disarmed and leave.
The sides also decided there would be an amnesty for all anti-government protesters.
But the separatists' spokesman in the city of Donetsk said that the Kiev government was "illegal", and vowed they would not go until it stepped down.
The protesters also insisted that pro-European Union demonstrators in Kiev's Maidan Square - the vanguard of the protest movement that toppled President Viktor Yanukovych, an ally of Moscow - had to pack up their camp first.
After cautiously welcoming the deal struck on Thursday, the White House has now stepped up pressure on Russia to use its influence over separatists occupying the buildings in nine cities and towns in eastern Ukraine.
On Friday, US National Security Adviser Susan Rice warned that if Moscow failed to uphold the deal a new round of sanctions would focus on what she called "very significant sectors of the Russian economy".
"We believe that Russia has considerable influence over the actions of those who have been engaged in destabilising activities in eastern Ukraine," she told reporters at a news briefing in Washington.
"If we don't see action commensurate with the commitments that Russia has made yesterday (Thursday) in Geneva... we and our European partners remain ready to impose additional costs on Russia."
She added that the US had identified close associates of the Russian leadership as potential targets for new sanctions.
US Secretary of State John Kerry spoke to Russian counterpart Sergei Lavrov by telephone on Friday.
A senior US state department official said Mr Kerry had made it clear "that the next few days would be a pivotal period for all sides to implement the statement's provisions".
However, the US government would not confirm a report in the Washington Post quoting Poland's Defence Minister Tomasz Siemoniak as saying that the US would soon announce the deployment of US ground forces to Poland in response to the Ukraine crisis.
The Pentagon said the US was "considering a range of additional measures we could take to bolster air, maritime and ground readiness in Europe" but that "we have nothing specific to announce at this time".
Ms Rice also said President Barack Obama had "expressed his disgust" at "utterly sickening" notices sent to Jews in Donetsk, demanding that they register themselves as Jewish.
The pamphlets, which purport to be from the pro-Moscow authorities in Donetsk, have caused alarm in the Jewish community, although their authenticity has not yet been verified.
Russia responded to the threat of further sanctions by saying it was disappointed with the US assessment of the Geneva deal.
"You can't treat Russia like a guilty schoolboy who has to... show he has done his homework," President Vladimir Putin's spokesman, Dmitry Peskov, said.
"That kind of language is unacceptable."
The foreign ministry also accused US officials of seeking to "whitewash" what it said was the use of force by the Kiev authorities against protesters in eastern Ukraine.
Ukraine's interim authorities have appealed for national unity and promised to meet some of the demands of pro-Russian protesters.
These include the decentralisation of power and guarantees for the status of the Russian language.
Speaking to the BBC, Ukrainian Foreign Minister Andriy Deshchytsia said the aim of the military operation in the east was to "bring life back to normal and protect the population".
He added that, unlike the separatists in eastern Ukraine, the pro-European protesters in Maidan Square had "asked permission from the city council" and their camp was therefore not an "illegal occupation".
A statement from the Donetsk separatists earlier said: "We cannot accept the values of the Kiev junta, we have our heroic past going back to World War Two, we are the Russian bear which is waking up".
It added: "Don't worry, everything will stay peaceful and orderly. The only problem is if the Kiev junta want war."
Ukraine has been in crisis since President Yanukovych was toppled in February.
Russia then annexed the Crimean peninsula - part of Ukraine but with a Russian-speaking majority - in a move that provoked international outrage.
The annexation followed a referendum in Crimea that backed a move to join the Russian Federation.