European Commission President Jose Manuel Barroso called for an immediate end to the violence and warned of possible consequences.
"We are generally concerned about where these developments are taking Ukraine," he said. "And we are continuing to follow closely these developments, as well as assessing possible actions by the European Union and consequences for our relations with that country."
EU foreign policy chief Catherine Ashton also strongly condemned the escalating violence.
The Polish Foreign Ministry has summoned the Ukrainian ambassador over the violence.
Russian Deputy Foreign Minister Grigory Karasin accused the "extremist opposition" of violating the constitution. Referring to U.S. and European statements, he said Ukrainian authorities "face outside interference."
The U.S. Embassy said Washington had revoked the visas of several Ukrainians linked to violence against protesters. No names were released.
WATCH: Protester's Body Leaves Hospital
Earlier in the day, police used tear gas, rubber bullets, and truncheons against protesters and also brought in an armored personnel carrier to help clear barricades. Protesters responded by throwing stones and petrol bombs and setting tires and garbage alight, sending thick black smoke into the sky.
The site of the continuing clashes, which entered their third day on January 22, is not far from Kyiv's Independence Square, where antigovernment protesters have been rallying peacefully for more than two months.
The latest violence erupted as Ukraine marked National Unification Day -- the day in 1919 that brought together the eastern and western parts of the country.
With reporting by AFP, pravda.com, Reuters, and AP
Copyright (c) 2014. RFE/RL, Inc. Reprinted with the permission of Radio Free Europe/Radio Liberty, 1201 Connecticut Ave., N.W. Washington DC 20036.