Even in a country where public lynchings have become a regular occurrence, it proved some acts of inhumanity still have the power to shock.

Ten minutes after Catherine Samba-Panza, the interim president of the Central African Republic (CAR), addressed the army at a hopeful ceremony, some of its members broke ranks to stab, stamp and pelt a man to death, drag his corpse through the streets and set it on fire, then film it on their phones.

The killing illustrated the fragility of Samba-Panza's authority over a nation torn by sectarian loathing and violence. Among the deepening crises are accounts of towns where the entire Muslim population has fled or been killed and allegations that supposedly neutral African peacekeepers are siding with rebel leaders.

At Wednesday's ceremony in the capital, Bangui, hundreds of uniformed soldiers in the national army – which had fallen apart after a coup almost a year ago – stood to attention as Samba-Panza, who was elected last month, spoke of her "pride in seeing so many elements of the Central African Republic Forces reunited".

But soon after she left, the mood quickly turned as the soldiers spotted a man they suspected of belonging to the largely Muslim rebel group known as the Seleka.

An Associated Press (AP) journalist at the scene reported: "His name was Idriss, and he was standing among them. They accused him of being an infiltrator, there to spy for Seleka. Out came the first knife. 'I will kill him with my own hands,' shouted one man who had come to enlist in the national army.

"The very men expected to protect civilians used knives, bricks and their own feet to attack the man. Troops from the tiny African nation of Burundi surrounded the wounded man to protect him from the growing crowd. He lay wounded on his back and still alive for about five minutes."

Interim president Catherine Samba-Panza greets the commander of French peacekeepers. Photograph: Laurence Geai/NurPhoto/Rex

The AP report continued: "But as the crowd moved closer, the peacekeepers withdrew, not even firing warning shots. The attack resumed. Some stabbed him while others kicked him in the face. Still others pelted him with concrete blocks as a crowd cheered.

"A police officer jumped out of his truck to try to halt the gruesome attack and was accosted by the crowd and accused of being a traitor. Senior officers managed to extract him from the mob and sped away with him in their pickup. The crowd dragged Idriss's corpse through the street, dismembered it and set it ablaze."

For more than half an hour, large crowds including children stood and watched the body burn, filming it on their phones, according to researchers from Human Rights Watch. When French forces arrived at the scene, they told the crowd to disperse, and reacted with horror when a young man walked up to them holding the severed leg of the lynching victim and then threw it on the fire.

Peter Bouckaert, the emergencies director at Human Rights Watch, said: "What should have been a moment of hope for the security of the Central African Republic turned into a horrific scene of bloodletting and mutilation. It is absolutely essential for President Samba-Panza to condemn this act of barbarity and prosecute the attackers."

Bouckaert and his colleagues said that in the past two weeks in Bangui they had witnessed mobs carrying out two lynchings and observed three other attempts that peacekeepers prevented.

In one case, they said, the Human Rights Watch team placed their car between a mob and its intended victim and took him to safety at a nearby Rwandan peacekeepers' base.

The coup in March 2013 triggered months of turmoil and bitter hatred toward the Seleka, leaving anyone accused of collaborating with them vulnerable to attack. The rebels' 10-month rule was marked by human rights abuses, and sparked a Christian armed movement known as the Anti-Balaka, which also has been accused of atrocities.

Christians form the majority in the CAR and in recent weeks most of the attacks in Bangui have targeted Muslims, forcing many to flee. Other towns have emptied of Muslims altogether.

On Wednesday Bouckaert posted on Twitter: "At 1730 hrs on Feb 5, Bozoum's historic Muslim presence ceased 2 exist, 2,100+ remaining Muslims evacuated 2 Chad in 16 trucks 12 pickups."

A street vendor in a refugee camp at Bangui airport. Almost a million people have been displaced by fighting and many towns have been emptied of Muslims. Photograph: Siegfried Modola/Reuters

Human Rights Watch has also said the Seleka rebels are regrouping in the north-east and accused Chadian peacekeepers of aiding the movements of Seleka leaders. "If the African Union is truly going to protect civilians in the Central African Republic, it needs to rein in the rogue activities of the Chadian peacekeeping troops," Bouckaert added.

There are now 5,000 African peacekeepers and 1,600 French troops on the ground. The UN children's agency, Unicef, has urged the international community to do everything it can to prevent the "human tragedy" in the CAR from turning into "a human catastrophe". Samba-Panza has pledged to "fully secure the greater part of the country" within a month.

Caesar Poblicks, an analyst at the London-based consultancy Conciliation Resources, said one of the greatest challenges facing Samba-Panza was a sense of triumphalism among the Anti-Balaka. "They feel like they brought about all the recent changes and the triumphalism is turning to defiance," he said.

"They were attempting to demand a ministry of defence position at their meeting with Samba-Panza. They have even objected to the choice of sports minister. Someone needs to be assertive enough to say: 'Anti-Balaka, you are not the CAR army'."

On Wednesday Bouckaert tweeted poignantly: "Painful 4 me 2 report on #CARcrisis endless atrocities--have @UCSB degree in African Studies, deeply believe in Africa's humanity, beauty."