French troops came under fire as they began disarming militias and rebels in the capital of the Central African Republic, Bangui, on Monday.

Soldiers taking part in Operation Sangaris reported a brief exchange of fire with members of the Séléka, a mostly Muslim coalition of former rebels, around the city's airport, a military official said.

Around 1,600 French soldiers have been deployed in the CAR to halt violent reprisals between religious factions that have left at least 465 people dead since last Thursday, according to the Red Cross.

The French troops, supported by helicopters and working alongside an African peacekeeping force, have ordered all militias and rebels to hand over their weapons.

The French defence minister, Jean-Yves Le Drian, said the period of immunity was over. Ex-rebel fighters had to return to barracks, and the rest would have to surrender their weapons. "First we'll ask gently and if they don't react we'll do it by force. The operation will take some time," he told French journalists.

The RAF has offered two large C-17 transport planes to help deploy French troops and armoured cars to the Central African Republic. One British plane arrived in Bangui on Friday and a second will arrive by Tuesday morning, according to UK defence officials. Britain provided the French with similar help in its efforts against al-Qaida militants in Mali earlier this year.

Chuck Hagel, the US secretary of defence, has ordered the US military to transport Burundian troops to the Central African Republic. Earlier on Monday a US official told Reuters the US had received a request for military support and this was likely to resemble the assistance it offered France in Mali this year, which included airlifts and intelligence sharing.

Colonel Gilles Jaron, a spokesman for the French forces, said the operation was going "mostly well", despite previous reports of palpable tension between French soldiers and armed groups. However, officers admitted some gunmen had removed their camouflage and uniforms and adopted civilian clothing to avoid being stopped.

"In some places the armed groups have given up and gone back to their barracks, in others they have given up their weapons," Jaron said. He said the exchange of fire around the airport had been brief. "There was shooting and a reply," he said. No one was injured.

Celestin Christ Leon, a spokesperson for the regional African force based at the airport, told Reuters: "The Séléka didn't want to disarm. There was a brief exchange of fire, and they ran away."

Paris has said its forces, backed by a UN security council resolution, are in the CAR to stop the inter-religious bloodshed, re-establish security, disarm the gunmen and protect the 300 French nationals present.

Operation Sangaris is aimed mostly at the Séléka, who overthrew president François Bozizé in March. Bozizé had been in power since a coup in 2003, and had been returned to power in a contested election in 2011.

The French foreign minister, Laurent Fabius, told French radio the disarming operation was complicated. "The difficulty is that many ex-Séléka have taken off their fatigues and dressed as civilians … it's difficult to recognise these individuals," he said. "We have explained to one and all, on the radio and by different media available, that they have to hand in their weapons. President [Michel] Djotodia has said the same thing. So we will engage with them and if that doesn't work, force will be used."

At Bossangoa, 200 miles north of Bangui, clashes between Christian and Muslim militias were said to have left 38 dead. A further dozen killings were reported in Bozoum and Bocaranga, in the north-west of the country.