The fighting took place in the eastern parts of the country on Thursday following the killing of two Muslims by Christian militias.
Twenty-one people were killed in clashes on Wednesday between the mostly Muslim Seleka group and Christian militia in the town of Bambari and Liwa village. The violence also left over 100 houses burned to the ground.
According to security forces, more than 30 people were injured in clashes that broke out on Monday and Tuesday in Liwa village.
The government recently asked the International Criminal Court (ICC) to investigate crimes being committed in the country over the past two years.
The African country descended into chaos last December, when Christian armed groups launched coordinated attacks against the Seleka group that toppled the government in March 2013.
On December 5, France invaded its former colony after the United Nations Security Council adopted a resolution giving the African Union and France the go-ahead to send troops to the country.
In March, UN Under-Secretary-General for Humanitarian Affairs and Emergency Relief Coordinator Valerie Amos said almost all of more than 100,000 Muslims once residing in the capital, Bangui, had fled the violence perpetrated by Christian militiamen.
People in the African country have recently protested against French forces and other international troops for failing to disarm rebels and curb the violence. Anti-French sentiments are running high both among the Christian and Muslim populations.