A Pentagon spokesman told the BBC on Friday that the incidents had happened mainly near the border with Russia, but gave no further details.
Earlier, pro-Russian separatists seized a bus carrying international military observers, Ukrainian officials said.
Talks were under way to secure their release near the town of Sloviansk.
Russia has tens of thousands of troops deployed along its side of the border with Ukraine as pro-Moscow separatists continue to occupy official buildings in a dozen eastern towns, defying the government in Kiev.
Also on Friday, US President Barack Obama and European leaders threatened to impose new sanctions on Russia, saying it has failed to implement an agreement to defuse the crisis in Ukraine.
Russia has accused the West of wanting to “seize” Ukraine.
In a statement from the Pentagon, Col Steven Warren repeated US calls to take “immediate steps to de-escalate the situation”.
Mr Hagel described Russian activity along the Ukrainian border as “dangerously destabilising” and “very provocative”.