Tens of thousands of people in Ukraine have held rival pro-unity and pro-Russian rallies, as Moscow continues to strengthen its grip on Crimea.
Pro-Russia supporters beat up their opponents in Sevastopol, Crimea.
In the eastern city of Luhansk, pro-Russian activists seized regional offices forcing the governor to resign.
UK and German leaders telephoned Russian President Vladimir Putin to urge him to pull back from Crimea. The region is to vote to secede next week.
Addressing a huge crowd in Kiev to mark the 200th birth anniversary of national poet Taras Shevchenko, Ukrainian Prime Minister Arseniy Yatsenyuk pledged not to give a "single centimetre" of Ukrainian land to the Kremlin.
Ukraine's defence minister has said Kiev has no plans to send the army to Crimea.
In other developments on Sunday:
- President Obama invites Mr Yatsenyuk to the White House, in what BBC correspondents say is a clear sign the new leader has support from Washington
- In the eastern city of Donetsk, pro-Russian protesters take down a Ukrainian flag near the regional government building, replacing it with a Russian flag
- In Kharkiv, also in the east, some 10,000 people reportedly march to support Ukraine's unity, chanting "No to war!" and "Ukraine, Kharkiv, Crimea!"
- Russia's ex-tycoon Mikhail Khodorkovsky, who spent a decade behind bars, accuses Moscow of being complicit with Ukraine's ousted government in using deadly violence against protesters
- In Yevpatoriya, western Crimea, pro-Russian forces threaten to storm the command point of a Ukrainian anti-aircraft missile unit if the personnel there do not surrender their weapons, a representative of the base tells BBC News
In Sevastopol, the violence erupted when pro-Russian groups attacked dozens of people guarding the Shevchenko rally.
The crowd threw missiles at a car as the activists tried to flee the scene, smashing windows. A BBC reporter in Sevastopol described the scenes as very ugly.
Some of the attackers were Russian Cossacks with whips.
The rally was attended by about 200 people.
A rival pro-Russian demonstration was also staged in the city - the base of Russia's Black Sea Fleet.
Moscow has been tightening its military grip on the Crimean peninsula.
Mr Putin has insisted he has the right to protect Russian interests and the rights of ethnic Russians there.
Mr Putin said "the steps taken by Crimea's legitimate authorities are based on international law".
However, German Chancellor Angela Merkel told him on Sunday that she considered the 16 March referendum on whether to secede from Ukraine and join Russia illegal.
Unrest in Ukraine erupted in November, following former President Viktor Yanukovych's last-minute rejection of a landmark EU deal in favour of a bailout from Russia.
Mr Yanukovych was ousted last month, and a new government has been voted in by the Ukrainian parliament.
Presidential elections are scheduled for 25 May.