The mayor of Ukraine's second-largest city, Kharkiv, is in serious condition after being shot by a sniper.
Government officials say Hennady Kernes was bicycling on the outskirts of the eastern Ukrainian city when he was shot in the back by an unidentified gunman.
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 who are calling for votes on independence for eastern Ukraine.
Kharkiv officials say Kernes is in the hospital "fighting for his life."
Meanwhile, the Pentagon says U.S. Defense Secretary Chuck Hagel spoke with Russian Defense Minister Sergei Shoygu by telephone Monday, wanting to know what Russia's intentions are towards Ukraine.
A Pentagon spokesman says Shoygu assured Hagel that Russian forces will not invade.
The spokesman also said Hagel reverberated Ukraine's right to preserve law and order and repeated his call for an end to what he calls Russia's destabilizing influence in Ukraine. Hagel waned that Russia faces further isolation if its aggression continues.
Also Monday, pro-Russian gunmen took control of government buildings in Kostyantynivka, the latest city they have seized in the eastern and southern part of the country. The separatists earlier seized government buildings at least 10 other cities, and are demanding a referendum on whether to secede from Ukraine and join Russia.
On Sunday, pro-Russian separatists in the eastern city of Luhansk declared the establishment of a "Luhansk People's Republic."
Meanwhile, European officials are trying to negotiate the release of a group of monitors detained by pro-Russia insurgents.
The monitors from the Organization for Security and Cooperation in Europe appeared in public with armed rebels watching Sunday to give assurances they are not being mistreated. The leader of the monitors, German Colonel Axel Schneider, assured reporters in Slovyansk they were in good health.
The insurgents called the eight military observers "prisoners of war."
The OSCE sent a team of negotiators to eastern Ukraine to meet with the self-proclaimed mayor of Slovyansk, Vyacheslav Ponomaryov, about freeing the military monitors, and one Swedish observer was released.
The rebels also displayed three bloodied and blindfolded officers from Ukraine's Security Service it captured. The officers were shown with heads bowed, and stripped of their pants and shoes.