(Adds new death toll, more colour, details)
By Natalia Zinets
KIEV, May 2 (Reuters) - At least four people were killed and several wounded in running battles between pro-Russian activists and supporters of Ukrainian unity in Odessa, deepening rifts in the largely Russian-speaking city.
The opposing sides have clashed before in the Black Sea port, but the battles have never resulted in deaths and some residents said they feared both may now try to seek retribution, possibly escalating the worst violence in the city since President Viktor Yanukovich was ousted in February.
The regional police said another man had been killed in fighting that spread across the city, taking the death toll to at least four after a march by the pro-Kiev demonstrators was ambushed. Petrol bombs, paving stones and explosive devices were thrown during the clashes, they said.
Waving the blue and yellow Ukrainian flag, wearing helmets and holding batons, thousands of Ukrainians took to the streets to march in support of the pro-Western authorities in Kiev. Some were supporters of the local football team, Chornomorets.
In an attack tinged with football rivalry, pro-Russian activists, many wearing the colours of team Metalist from the eastern Kharkiv region, waded into the crowd.
Police soon lost control. They said the trade union building was set later alight.
Dmytro Spivak, a local parliamentarian, told Ukrainian television that at least six young supporters of the authorities in Kiev had been killed.
"It is abundantly clear that the pro-Russian side was very well armed, well organised and that this action was planned long ago," he said, adding the police did little to stop the clashes.
"I will say one thing to (Russian President Vladimir) Putin; forget about Odessa."
Ukraine's new pro-Western leaders have accused Moscow of supporting pro-Russian groups to try to destabilise a country desperately trying to recover from months of upheaval that led to the toppling of Yanukovich.
The Kremlin denies playing any role in the uprisings in the east and south of Ukraine, saying Russian-speakers there are simply protecting their rights against possible assault by Kiev's pro-Western leaders. (Additonal reporting by Elizabeth Piper, writing by Elizabeth Piper, editing by Mark Heinrich and Nigel Stephenson)