The CAR army, with the support of French, Russian, Rwandan and UN forces, has been fighting for some time against groups that tried to disrupt the December 27 presidential election, in which Fosten Arkanz Tuadera was declared the winner.
The rebels attacked cities near Bangui last month, but so far they have not been able to reach the capital.
This time, the rebels have attacked Bangui on several fronts, including its northern districts, Prime Minister Firman Ngrebada said.
The country, with a population of 4.7 million, has not been violent since the overthrow of President François Boziz in the 2013 uprising.
Thousands have lost their lives in violence, more than a million have been forced to flee their homes.
As a result of the latest outbreak of violence, more than 30,000 people have fled to neighboring countries, food shortages have risen and prices have risen in the capital.
Tuadera has been declared the winner of the election, but the opposition is demanding a repeat vote due to allegations of irregularities and insecurity, which has prevented voting in many places.