The Pentagon says Russian Defense Minister Sergei Shoygu has assured Defense Secretary Chuck Hagel that Russian forces will not invade Ukraine.
The two spoke by telephone Monday, with Hagel wanting clarification on Russia's intentions.
A Pentagon spokesman said Hagel emphasized how dangerous the situation is, and that Ukraine has the right to preserve law and order inside its borders. He reminded Shoygu that Russia faces more isolation if its aggression continues.
Hagel also asked for Russian help in freeing seven European inspectors held by pro-Russian separatists in eastern Ukraine.
Meanwhile, officials in Ukraine's second-largest city, Kharkiv, say Mayor Hennady Kernes is fighting for his life after being shot in the back by a sniper. Kernes was hit while riding his bicycle on the outskirts of the city.
Kernes opposed the popular protests in Kiyv that led to the ouster of President Viktor Yanukovych. But he has said he does not support pro-Russian separatists.
Also Monday, pro-Russian gunmen took control of government buildings in the city of Kostyantynivka. Separatists are now in control of Ukrainian government buildings in at least 11 eastern and southern cities. They are demanding referendums on whether to secede from Ukraine and join Russia.
A similar vote in Crimea last month led to Russia's annexation of that Ukrainian peninsula.