* Kharkhiv mayor fighting for life after shooting
* Supported pro-Russian separatists but recently changed views
* Police have forced rebels from buildings in city (Adds details)
KIEV, April 28 (Reuters) - The mayor of Ukraine's second biggest city was shot in the back on Monday, the highest profile assassination attempt in eastern Ukraine since a standoff between Moscow and Kiev began two months ago.
Gennady Kernes underwent two hours of surgery after the attack in Kharkiv, one eastern city where police have managed to dislodge pro-Moscow rebels. Surgeon Valery Boiko said his life would hang in the balance for the next few days.
Kernes, 54, went into politics after making his fortune in the gangster-ridden post-communist 1990s.
After protesters toppled pro-Moscow Ukrainian President Viktor Yanukovich in February, he supported calls for Kharkiv to become independent from Kiev's new, pro-European leaders.
But he changed his views after being accused of fomenting separatism and when Ukrainian police forced pro-Russian protesters out of administrative buildings in the city.
Iryna Kushchenko, spokeswoman for the local government, said Kernes was either riding his bicycle or jogging when he was shot by someone probably hidden in nearby woods. His bodyguards were following in a car but were not close enough to intervene.
Ukraine's deputy interior minister, Serhiy Yarovy, said they were investigating whether the shooting was in retaliation for the detention of 13 pro-Russian separatists on Sunday on charges of possession of petrol bombs, explosives and nails.
"One of the main versions (of events) is whether it was the reaction of separatists to recent events in Kharkiv," he said.
Kernes is one of Ukraine's most prominent Jewish politicians who according to his official biography started out working for state enterprises in the city before embarking on a series of business ventures including gas trading.
His friend, Mykhailo Dobkin, a candidate in Ukraine's presidential election on May 25, said investigators had found the bullet casing and were pursuing various leads.
"If I knew who did it, I wouldn't be standing here now. I would have my hands round his throat," he told journalists.
Kernes, who accumulated substantial wealth before entering politics, has declined to talk about his past. (Reporting by Christian Lowe and Natalia Zinets, writing by Elizabeth Piper; editing by Timothy Heritage and Philippa Fletcher)