* Rebels kill two, mob lynch five prisoners in reprisal
* Red Cross says finds 87 bodies in five days
* French troops involved in overnight fighting - source (Recasts with Wednesday's deaths, updates throughout)
By Emmanuel Braun
BANGUI, Jan 22 (Reuters) - Seven people died in inter-religious attacks and reprisal killings in Central African Republic's capital Bangui on Wednesday, a human rights campaigner said, underlining the challenge the new interim president faces in restoring peace.
The local Red Cross said it also found another 11 corpses, most burnt beyond recognition.
Close to one million people, or a quarter of the population, have been displaced in the former French colony by clashes that began when mostly Muslim Seleka rebels seized power in a coup in March.
Christian self-defence groups known as "anti-balaka" (anti-machete) have since taken up arms against them, and the United Nations estimates that tit-for-tat violence has claimed more than 2,000 lives.
Wednesday's violence erupted after Seleka fighters left a military base looking for food and shot and killed two Christians, Human Rights Watch (HRW) said.
In reprisal, "the youth from the neighbourhood went to the prison and took out five Seleka detainees and killed them," Peter Bouckaert, an HRW researcher in Bangui, told Reuters.
The other 11 bodies were found behind a military camp in another part of the city.
Antoine Mbao Bogo, president of the Central African Red Cross Society, said nine of the bodies collected in the mostly Muslim northern neighbourhood of PK11 had been set on fire.
"They were not buried, they were dumped on the ground," he told Reuters by telephone.
He added that the Red Cross had collected 87 bodies in the past five days across the country. The figure did not include the seven people killed on Wednesday.
OUT OF CONTROL
The arrival of a 1,600-strong French military mission and another 5,000 African Union peacekeepers has so far failed to stop the violence in Central African Republic.
A source with the French force said on Wednesday its soldiers were involved in overnight clashes after coming under attack from unidentified gunmen.
This week the European Union said it would send 500 soldiers to support international troops already on the ground. And the United States said on Wednesday it was giving an additional $30 million to help ease the country's crippling humanitarian crisis.
Interim President Catherine Samba-Panza, the mayor of Bangui, was appointed as leader on Monday and is due to formally take office on Thursday.
She replaced former interim President Michel Djotodia, a former Seleka leader who stepped down on Jan. 10 amid intense international pressure. Samba-Panza has pledged to meet with armed groups in an effort to restore order.
However, ending the cycle of violence will not be easy.
HRW researcher Bouckaert witnessed hundreds of Christians attack and embark on a looting spree in the mainly Muslim PK13 neighbourhood on Wednesday. Rwandan peacekeepers, newly arrived in the country, were forced to intervene to protect around 30 Muslim civilians surrounded by the mob until they were evacuated by French soldiers.
Elsewhere, a Reuters witness said that a crowd of angry Christian residents armed with machetes and wooden weapons gathered in the neighbourhood of Ngaragba, near the French embassy, to protest against ongoing attacks by Seleka.
The protesters burned tyres as French troops tried to contain them.
"Last night and even this morning they came to attack us. We don't know where we will live next," said former Corporal Bernard Desire Mariano, referring to Seleka attacks.
Aid workers said they could wind up struggling to feed Bangui's displaced population, including around 100,000 seeking shelter at the airport, because food supplies had been disrupted due to a strike by U.N. truck drivers. (Additional reporting by Marine Pennetier; Writing by Emma Farge and Joe Bavier; Editing by Mike Collett-White and Jonathan Oatis)