* Violence ebbs after a week that saw over 500 killed
* Deep distrust remains between Christians and Muslims
* French minister says mission more difficult than Mali
By Emmanuel Braun
BANGUI, Dec 11 (Reuters) - Religious leaders sought reconciliation between Muslims and Christians in Central African Republic on Wednesday during a lull in violence that has killed hundreds of people and drawn in French troops seeking to stop the bloodshed.
Fighters, both Muslim and Christian, have gone door to door murdering civilians over the past week. Mobs have carried out lynchings, set fire to cars and buildings and looted shops.
In the capital Bangui, religious leaders met to distribute food to the more than 10,000 displaced people huddled at a gathering at a community centre for protection.
"We are here because we are brothers first and foremost," Imam Oumar Kobine Layama, president of the Islamic Central African community, told the crowd of Christians.
"Today we are listening to the young to see what they propose because our house is burning down and we need to try to put out the fire," he said.
In an indication of the distrust between communities, many refused to take the offering of food in Layama's presence.
"Since we've been here, Muslims have never given us anything," said Missili Ndiaye, a displaced Christian living in the centre since the latest wave of violence. "We don't know what they've put inside it - it might be poisoned."
France has suggested it acted in Central African Republic because of fears of Muslim-Christian "genocide", evoking memories of Rwanda, where 800,000 Tutsi and moderate Hutus were killed by Hutu extremists in 1994 as the world stood by.
Central African Republic President Michel Djotodia, as well as regional analysts, have said the fears were exaggerated.
France boosted its military presence there to 1,600 soldiers in response to the wave of massacres that began last Thursday and has killed more than 500 people. Two French soldiers have been killed.
French Defence Minister Jean-Yves Le Drian said the complexity of the situation meant the mission could be harder than Mali, where French troops are still trying to rid the north of Islamist militants following an intervention in January.
"We have to disarm everybody otherwise the situation will not be manageable," he said on RMC radio on Wednesday.
"The (CAR mission) is much more difficult and delicate because identifying the enemy is not as simple (as in Mali) and there are members of Seleka and anti-Balaka that disappear into the population."
Chronically unstable Central African Republic has spiralled into chaos since mainly Muslim Seleka rebels seized power in March and embarked on months of looting, raping and killing.
Christian militias or anti-Balaka which have sprung up in opposition to Seleka, and gunmen loyal to ousted president Francois Bozize attacked Bangui on Dec. 5 setting off this round of violence, the worst since the crisis began.
Taking advantage of a lull in the fighting, some shopkeepers and taxis returned to work on Wednesday in the riverside capital, as French helicopters and war planes monitored from above. But tensions were never far from the surface.
In other parts of the capital, aid workers and residents began to make preparations for burials in mass graves.
Joseph Bindoumi, president of the Central African League for the Defence of Human Rights, said that a grave for 100 had already been dug to the south of Bangui. Muslims and Christians will be buried separately, the Red Cross has indicated.
"We are now trying to reconcile people and to help boost morale," Bindoumi said.
Even before the latest violence, diamond-rich Central African Republic was in a state of chaos as ex-rebel leader Djotodia struggled to keep control of his loose band of militia since seizing power.
The United Nations estimates that the total number of displaced countrywide has risen to half a million since the crisis began a year ago.
Medical charity Medical Charity Medecins Sans Frontieres said that an improvised centre for more than 20,000 displaced people at Bangui airport was lacking food, shelter and toilets.
The charity received around 12 new patients on Wednesday, down from 72 people received the previous day, it said.
In the PK 5 neighbourhood, residents struggled to contain their anger following an attack on a mosque earlier this week.
"It's all destroyed ... If they (the Christians) don't want us then maybe we should just divide the country: they take one side, and we take another," said resident Aboubacar Amadjoda. (Additional reporting by Emma Farge and John Irish; Writing by Emma Farge; Editing by Joe Bavier and Alison Williams)