Army spokesman Major Adolphe Manirakiza said 46 National Liberation Forces (FNL) rebels were killed and 30 rifles seized by the army in a major operation in the town of Nyabiraba, 25km southeast of Bujumbura, on Saturday.
"We also suffered the loss of three soldiers," he said.
The mainly Hutu FNL is the last rebel group still operating in Burundi, which is emerging from an 11-year civil war that has taken more than 300,000 lives.
Manirakiza said the army operation was launched after the FNL attacked a position of the Hutu Forces for Defence for Democracy (FDD) which, after opposing the peace process, has joined the government.
The FNL could not be contacted on Sunday about the fighting, which local officials said had also caused 30,000 people to flee the area.
Burundi's civil war was triggered by the assassination in October 1993 of Burundi's first elected Hutu president Melchior Ndadaye by the army, dominated by the Tutsi minority.
"In the past weeks, small FNL groups have infiltrated Burundi from the east of the DRC [Democratic Republic of Congo] to come here and mark their presence"
Major Adolphe Manirakiza,
Burundi army spokesman
The assassination triggered a rebellion from the Hutu majority which developed into a civil war.
Fighting came to an end last year when the main rebel force reached a peace deal with the transitional government set up under an accord signed at Arusha in neighbouring Tanzania in 2000.
But after several months of calm, the FNL has renewed attacks in the rural region around Bujumbura.
Tutsi refugees killed
A soldier and three FNL rebels were killed last week in a rebel attack near Bujumbura in the first such attack close to the capital in six months, Manirakiza said.
"In the past weeks, small FNL groups have infiltrated Burundi from the east of the DRC [Democratic Republic of Congo] to come here and mark their presence," he said.
The surge in violence in Burundi
has broken months of calm
"But we are present on the ground and we will end this quickly," he added.
The FNL has been designated a terrorist group by countries in the African Great Lakes region after they claimed responsibility for the murders in August of 160 Tutsi refugees in western Burundi.
The country is in a transitional phase of government which is due to end in April with presidential elections, but plans for a referendum on a new constitution have already been pushed back three times.