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Ukraine said the Odessa force, based on "civil activists", would replace local police who had failed to tackle rebel actions at the weekend. Its dispatch was a clear signal from Kiev that, while tackling rebellion in the east, it would vigorously resist any sign of a slide to a broader civil war.
Odessa, with its ethnic mix from Russians to Ukrainians, Georgians to Tatars a cultural contrast to the pro-Russian east, was quiet on Monday. Ukrainian flags flew at half mast for funerals of some of the dozens killed in clashes on Friday.
But in the east, fighting intensified around the pro-Russian stronghold of Slaviansk, a city of 118,000, where rebel fighters ambushed Ukrainian forces early in the day.
The Interior Ministry said five paramilitary police were killed. Separatists said four of their number had also died.
The sound of an air-raid siren could be heard in the centre of Slaviansk, and a church bell rang in the main square.
Russia's foreign ministry called on Kiev to "stop the bloodshed, withdraw forces and finally sit down at the negotiating table". It also published an 80-page report detailing "widespread and gross human rights violations" in Ukraine over the past six months for which it blamed the new government and its Western allies.
CONCERNS FOR KIEV
Russia denies Ukrainian and Western charges it is seeking to undermine the country of 45 million and using special forces to lead the insurgency, as it did before annexing Crimea in March.
German Foreign Minister Frank-Walter Steinmeier said he feared neither side could now control forces unleashed.
"I'm convinced we are struggling against a situation that has taken on a dynamic of its own. There are groups in eastern Ukraine that are not listening to either Kiev ... or Moscow."
The self-declared pro-Russian mayor of Slaviansk Vyacheslav Ponomarev told Reuters by telephone: "(The Ukrainians) are deploying ever more forces here. Recently there was a parachute drop... For us, they are not military, but fascists."
Ukraine's Defence Ministry said rebels had shot down a military helicopter, the fourth since Friday, with heavy machine gun fire. The helicopter crashed into a river and the crew was rescued but there were no details of their condition.
Diana, 15, who lives near Slaviansk in a single-storey house at the strategic junction of the road between Kharkiv and Rostov, said she saw Ukrainian tanks fire on rebel cars. A fuel tank at a petrol station exploded and fighters fired at houses.
"My father was injured in the head by glass splinters. It's terrifying. There's just nowhere to live now. Everything is broken, our television, our computer; they shot at our car."
The violence in Odessa marked a watershed for Ukraine.
It increased fears that trouble could spread to the capital in the approach to Friday's celebrations of the Soviet victory in World War Two, an event that could kindle tensions over Kiev's relations with its former communist masters in Moscow.
Over 40 people were killed in Friday's clashes, the worst since pro-Moscow president Viktor Yanukovich fled to Moscow in February amid protests by Ukrainians demanding closer ties to Europe. Most were pro-Russians killed when the building they occupied was set ablaze by petrol bombs.
It is not clear who started the fire, but Moscow accuses Kiev of inciting violence.
On Sunday, hundreds besieged a police station where fellow pro-Moscow activists were held after street fighting that led up to the house blaze. Police freed 67 of them, infuriating Kiev.
"The police in Odessa acted outrageously," Interior Minister Arseny Avakov wrote on his Facebook page. "The 'honour of the uniform' will offer no cover."
He said he had sent the newly formed Kiev-1 force to Odessa after sacking the entire Odessa force leadership.
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.
Alexander, a man in his mid-20s who said he took part in the anti-Kiev actions, agreed with Avakov that police had done nothing.
"But this special new battalion, they're stormtroopers from Western Ukraine who'll be hunting our people all over the city."
ODESSA'S ECONOMIC IMPORTANCE
Loss of control of Odessa would be a huge economic and political blow for Ukraine, a country the size of France that borders several NATO countries and aspires to join the military alliance, a primary source of concern for the Kremlin.
A city of a million people, with a grand history as the cosmopolitan southern gateway for the tsars' empire, Odessa has two ports, including an oil terminal, and is a transport hub.
Many on the city's streets were shocked by the violence.
"People who brought this to our city were not and are not and will not be true citizens of Odessa," said Alexei, 40, an ethnic Russian. "We are Odessa, and this is a special place."
Rabbi Fichel Chichelnitsky, an official with Odessa's 70,000-strong Jewish community, said: "I'm hoping these deaths serve as a stern warning to everyone that this is not a game."
The chant "Odessa is a Russian city!" was heard at pro-Russian demonstrations through the weekend.
Many Russians agree. Founded by Empress Catherine the Great, it has played a key role in Russian imperial history.
Soviet film director Sergei Eisenstein set scenes of a massacre of civilians during a 1905 uprising on the grand steps that sweep down to the port. The images from "The Battleship Potemkin" are among the most famous in cinema history.
Diplomacy continued over the weekend.
Germany said on Sunday it was pressing for a second meeting in Geneva to bring Russia and Ukraine together with the United States and European Union. Moscow and Kiev accuse each other of wrecking an earlier accord on April 17.
Berlin said it was doing what it could to make sure a presidential election planned for May 25 went ahead.
"The election would be not just a means for stabilisation but also a strong signal for a better future for Ukraine," Chancellor Angela Merkel's spokesman Steffen Seibert said.
He said a referendum planned by pro-Russian separatists in the eastern city of Donetsk, where rebels have proclaimed a "Donetsk People's Republic", would only increase tensions.
Certainly, failure by Kiev authorities to conduct the election in rebel-controlled eastern cities would give Moscow grounds to question the legitimacy of any government emerging, just as it challenges the present administration.