* Spokesman for AU force says protesters fired first on peacekeepers
* Protesters say they were unarmed
* Wednesday's attack on church has sharply raised tensions in capital (Adds details)
By Crispin Dembassa-Kette and Serge Leger Kokpakpa
BANGUI, May 30 (Reuters) - At least two people were shot dead on Friday by Burundian peacekeepers who clashed with protesters in the capital of Central African Republic, in a second day of violent demonstrations after an attack on a church ignited tensions.
A spokesman for the African Union peacekeeping mission said Burundian troops returned fire after being shot at by members of a crowd calling for their departure and the resignation of interim President Catherine Samba-Panza.
However, the protesters said they were unarmed and had come to hold talks with the head of the U.N. mission, which has its headquarters nearby.
"There were some armed demonstrators and they attacked the Burundian base. The Burundians responded with live fire and there were two people killed and two wounded amongst the assailants," Francis Che, spokesman for the African Union mission (MISCA), told Reuters by telephone.
"The crowd has dispersed. We recovered two weapons and a hand grenade."
Demonstrators had gathered outside the headquarters of the U.N. mission in Bangui - which is some 200 metres (yards) from the Burundian base - from around 5 a.m. (4 GMT) on Friday, demanding the departure of the Burundian troops, whom they accuse of favouring Muslims.
Protesters told Reuters TV that five people were killed in the clashes.
"We gathered here this morning, with women and children and with no weapons, and the Burundians have killed five people," said Eric Sako, a businessman. "We were in the U.N. offices trying to explain things, and they opened fire on us."
Frustration is running high at the failure of the interim government and some 8,000 African Union and French peacekeepers to return peace to country. It was stoked by Wednesday's attack on the Fatima church by Muslim gunmen in which some 15 people killed.
Youths burnt tyres at roadblocks on main roads in Bangui on Friday while, in several neighbourhoods, residents beat pots and pans in an early morning protest, and others fired guns into the air. French peacekeepers used bulldozers to remove the barricades on Friday.
The country has been gripped by ethnic and religious violence for more than a year since Seleka rebels, who are mostly Muslim, seized Bangui in March 2013. The Seleka left power in January under international pressure and since then the anti-balaka militias have attacked on Muslims.
Those attacks have largely driven Muslims from the capital and areas to the west, effectively partitioning Central African Republic, whose northeast is controlled mainly by Seleka.
Following Wednesday's attack on the Fatima church, Sebastien Wenezoui, a leader of the anti-Balaka Christian militia, accused international forces of abandoning the church to its attackers and singled out Burundian soldiers and French soldiers for being too slow to respond. (Additional reporting by Hubert-Mary Djamany in Bangui and Daniel Flynn in Dakar; Writing by Daniel Flynn; Editing by Bate Felix)