* New president urges militia to lay down arms
* 16 killed, mostly victims of xenophobic mobs - Red Cross
* French troops shoot dead one man, say they were fired upon (Updates death toll, adds Red Cross quote, new president's inauguration speech)
By Emmanuel Braun and Paul-Marin Ngoupana
BANGUI, Jan 23 (Reuters) - At least 16 people died in clashes in Central African Republic on Thursday as new interim president Catherine Samba-Panza took office with a plea for militia to lay down their arms to halt the escalating inter-religious violence.
Almost one million people, or a quarter of the population of the former French colony, have been displaced by fighting that began when gunmen from the Seleka rebels, most of them Muslims, seized power in a coup in March.
Christian self-defence groups, known as "anti-balaka" (anti-machete), have since taken up arms against them. The United Nations estimates that tit-for-tat violence has claimed more than 2,000 lives since March.
A French intervention force and thousands of African peacekeepers have failed to stop the killing, which has worsened in Bangui and in the northwest in recent days. At least 16 died in the capital on Thursday, the Red Cross said.
Samba-Panza, the mayor of Bangui elected as interim president by a transitional assembly on Monday as part of a plan to restore order, said she was taking the helm of a country in chaos.
"It is urgent that state authority and security is re-established throughout the entire country," she said in her inaugural speech, in the presence of French Foreign Minister Laurent Fabius and regional leaders.
"I call on the anti-balaka to show patriotism and lay down their arms. This permanent disorder will not be tolerated." She took office after Michel Djotodia, a former Seleka leader, stepped down on Jan. 10 after intense international pressure.
Hundreds of looters rampaged through Muslim areas of Bangui on Thursday, burning homes and carrying off furniture and metal roofs. Antoine Mbao Bogo, president of the country's Red Cross, said the northern PK12 neighbourhood was the epicentre.
"There are scenes of xenophobia where people are stabbing others because they belong to another ethnic group. There were 16 killed in an atrocious manner," he told Reuters.
French Defence Minister Jean-Yves Le Drian said on Thursday that international forces faced a difficult task to end the deepening cycle of violence.
"There is an unbelievable level of hatred. No doubt we underestimated the degree of hatred, the desire for vengeance among the Seleka and the anti-balaka militias," he told French TV channel iTele.
FRENCH KILL ONE MAN
French forces shot one man dead among a group protesting against the lack of security after anti-balaka fighters killed one person at a camp for displaced Muslims waiting to leave the city, witnesses said.
After the man was buried, an angry crowd armed with machetes and other crude weapons approached a French checkpoint in PK12, said Peter Bouckaert, emergencies director for Human Rights Watch.
"We saw them bringing the body back from the frontline where they were protesting and they said: 'It's the French. It's the French,'" Bouckaert said by telephone.
Another man was wounded in the shooting, Bouckaert said.
French army spokesman Colonel Gilles Jaron said a group of gunmen had attacked French forces, who responded. One of the gunmen was hit and his body was retrieved by his colleagues. Jaron did not say whether the French suffered casualties.
Samba-Panza has pledged to name a non-political cabinet of 18 technocrats and hold talks with armed groups in an effort to restore order..
She has called for more foreign troops to bolster a force that already includes a 1,600-strong French military mission and another 5,000 African Union peacekeepers.
Fabius played down the immediate likelihood of more French troops. "We have already made a major effort. We never say never, but it's firstly up to the international community to mobilise now," he told reporters in Bangui.
Some 500 additional troops pledged by European Union nations this week will help to secure Bangui's airport and surrounding area, freeing up French soldiers for patrols in the capital and throughout the country, Le Drian said.
The World Bank announced on Thursday that it would contribute $100 million in emergency development funds to help restore key government services and provide much-needed food, healthcare, and other vital supplies. (Additional reporting by Marine Pennetier in Paris; Writing by Matthew Mpoke Bigg and Joe Bavier; Editing by Daniel Flynn and Alister Doyle)