The White House said President Barack Obama urged Russian President Vladimir Putin in a phone call to agree to a peace deal.
"If Russia continues its aggressive actions in Ukraine, including by sending troops, weapons, and financing to support the separatists, the costs for Russia will rise," the White House statement added.
Russian Foreign Minister Sergei Lavrov has said any agreement on resolving the conflict in Ukraine must protect the rights of all citizens living in the country.
At a joint news conference with Greek Foreign Minister Nikos Kotzias, Mr Lavrov said there could only be a political situation to the conflict in eastern Ukraine, which has killed more than 5,000 people.
Mr Lavrov also accused the Ukraine military of trying to gain more ground in east Ukraine to "use as leverage" during peace talks in Minsk.
He added that control over the Russia-Ukraine border could not be used as a condition of peace as that issue needed to be agreed with pro-separatist rebels.
Video footage recorded from Kramatorsk, deep inside Ukrainian-government controlled territory, shows rockets landing on civilian areas.
Video footage appears to show the moment a shell strikes a community soup kitchen in eastern Ukraine.
A mother in eastern Ukraine buries her son - yet another casualty in a civil war that is killing civilians with appalling randomness.