Fighting continued near the eastern city of Slaviansk, where Ukrainian troops have been pressing a campaign to end pro-Russian rebellion.
Four Ukrainian paramilitary police were killed in fighting with pro-Russian separatists near the rebel stronghold of Slaviansk, the Interior Ministry said, in renewed violence Kiev is struggling to stop across the East.
The sound of an air siren could be heard in the centre of Slaviansk and a church bell rang in the main square. Gunfire seemed to be coming closer to the centre of the city.
Rebel fighters ambushed Ukrainian forces early yesterday, triggering heavy fighting on the outskirts of the city of 118,000, Interior Minister Arsen Avakov said.
A Reuters correspondent said gunfire seemed to be coming closer to the city centre.
The violence in Odessa, a south-western port with a broad ethnic mix from Russians and Ukrainians to Georgians and Tatars, was seen as a turning-point in Kiev, encroaching for the first time into an area beyond the Russian-speaking East.
Authorities fear trouble in Kiev in the approach to Friday's celebrations of the Soviet victory in the Second World War.
Interior Minister Arsen Avakov said the new Odessa force, "Kiev-1", was based on "civil activists" who wanted to help the Black Sea city "in these difficult days". The leadership of the local police has been fired and may face criminal action.
Friday's fighting in Odessa was the deadliest since Moscow-oriented President Viktor Yanukovich fled to Russia in February and pro-Russian militants launched uprisings in towns across the industrial east. More than 40 people were killed and Ukraine, a country of 45 million, appeared to be lurching to civil war.
"The police in Odessa acted outrageously, possibly in a criminal fashion," Avakov wrote on his Facebook page. Ukrainian leaders have made it clear they see the police force across wide areas of the country as unreliable in the face of rebellion they say is backed by Moscow and led on the ground by Russian special forces. The units Avakov referred to emerged partly from the uprising against Yanukovich early this year.
That could fuel anger among the government's opponents, who accuse it of promoting "fascist" militant groups, such as Right Sector, that took part in the Kiev uprising over the winter.