The Central African Republic's Muslim rebels and Christian militia accused each other on Tuesday of violating a ceasefire deal signed last month, following days of clashes in the country's remote north.

The signing two weeks ago in the neighbouring Congo Republic raised hopes of a political solution to sectarian violence that has killed thousands and displaced more than a million people since the Muslim Seleka fighters seized power in March 2013.

The Christian "anti-balaka" took up arms in response to a wave of abuses by Seleka fighters once in power last year, pushing the rebels back northward. Tens of thousands of Muslims fled militia violence into the Seleka-controlled enclave.

Seleka said militia leaders had launched a wave of attacks on their territory in the north following last month's signing. "The agreement was broken right after it was signed," said Seleka's Ahmat Nedjad, saying Muslims had been attacked in the towns of Dekoa, Bodo and Batangafo in late July.

A local radio station said two soldiers for the African Union peacekeeping force, MISCA, had been killed in the Batangafo clashes. A MISCA official declined to comment.

Brice Emotion Namsio, a spokesman for the anti-balaka, denied they were responsible for the violence, saying clear orders were given to militia commanders before the Brazzaville deal to cease their attacks.

In an apparent sign of the strain of the continuing violence on the country's interim government, a presidential spokesman said on Tuesday the cabinet had stepped down.

"The head of state asked for and obtained the resignation of the Prime Minister Andre Nzapayeke and his government," the spokesman said, without naming a new prime minister.

France has sent some 2,000 troops to the Central African Republic as part of its Sangaris peacekeeping force, in support of the 6,000-strong MISCA force. A French army official said its forces were attacked on Monday by about 100 fighters with anti-tank guns during a reconnaissance mission.

"The Sangaris force counter-attacked with Rafale fighter jets ... and helicopters," the official said. He said there were no injuries or deaths among the French soldiers and declined to name the armed group responsible for the attack.

Government spokesman Gaston Mackouzangba called on international peacekeepers to forcibly disarm militias in line with their mandates.

The renewal of violence in the Central African Republic is a blow to France, which had hoped the ceasefire agreement would pave the way for the organisation of elections and allow it to begin withdrawing troops.