The US, the EU, Russia and Ukraine Thursday brokered an agreement in Geneva to de-escalate tension in eastern Ukraine, where pro-Russian militants were occupying government buildings in some cities, and Ukraine's military operation had failed to flush them out, Xinhua reported.
The militants were refusing to heed the fresh deal, demanding the Kiev government step down as well.
"We expect and we will be watching whether Russia does or does not uphold its responsibility to use its very considerable influence to restrain and withdraw those irregular militia from the buildings and spaces that they've occupied," National Security Adviser Susan Rice told a White House press briefing.
"If we don't see action commensurate with the commitments that Russia has made yesterday in Geneva, which we all welcome, then obviously we've been very clear that we and our European partners remain ready to impose additional costs on Russia for failing to adhere to its obligations," she said.
State Department spokeswoman Jennifer Psaki insisted on the legitimacy of the Kiev government, saying its coming to power "was not a coup" but filling in "a vacuum of leadership" left by President Viktor Yanukovych Feb 22 when he fled the capital.
Russia does not recognise the Ukrainian government either, and President Vladimir Putin Thursday warned that as Ukraine was plunging into an "abyss," he had a "right" to send troops into the country but "very much hoped" that he would not have to do so.
Washington has targeted a number of key Russian and Crimean officials as well as a Russian bank following Moscow's adoption of Crimea from Ukraine last month.
President Barack Obama signed an executive order in late March authorising expanded sanctions against more individuals and entities as well as key sectors of Russia's economy including energy, banking, mining and defense in response to Moscow's further moves.