* Last Pride march attacked by nationalists and hooligans
* Serbia under pressure from EU over gay rights
* Church compares homosexuality to pedophilia and incest
BELGRADE, Sept 26 (Reuters) - Authorities in Serbia gave a conditional green light on Friday to the country's first gay Pride march since 2010, bowing to pressure from the European Union as the Balkan country pursues membership talks.
Serbia has banned Pride for the past three years, since hardline nationalists and football hooligans attacked marchers and fought running battles with police in Belgrade in 2010.
The EU says the event is a test of the Balkan country's commitment to the fundamental freedoms espoused by the 28-member bloc.
Interior Minister Nebojsa Stefanovic, after a meeting of Serbia's Security Coordination Bureau, said authorities had decided not to ban Sunday's march, but still reserved the right to do so if the threat to security was too great. Thousands of police are expected to secure the event.
Prime Minister Aleksandar Vucic appeared to give his own endorsement on Thursday, but said he personally would not take part.
"I respect the constitutional obligations of the state and my obligation to guarantee the safety and security of all people," Vucic told a news conference.
"It is my democratic right not to participate in Pride, nor do I have any intention of doing so."
Homophobia is widespread in Serbia and other conservative societies across the Balkans, often fueled by church leaders and right-wing political parties.
Vucic is a former ultranationalist who has rebranded himself as a pro-Western reformer. He has managed to retain the support of many traditionally conservative nationalists, while also hoping to open a first round of EU accession negotiations within months.
The head of Serbia's Orthodox Church, Patriarch Irinej, condemned Pride on Tuesday, asking why, if homosexuality was "propagated, then why not also pedophilia, which is widespread in the West, and incest?" (Reporting by Matt Robinson; editing by Andrew Roche)