"Since this morning, our troops have already conquered several of their targets which has been controlled by the FNL," a military spokesman said.
He said that the army was still encountering some pockets of resistance.
The Burundian army has also deployed reinforcements to the Isale area since Sunday as part of a major operation against the FNL.
Artillery fire could be heard as far as Bujumbura, where the recent fighting has been concentrated, an AFP correspondent reported.
At least 49 people are estimated to have died since the FNL launched a major offensive on April 17, according to a toll compiled from army and medical sources.
The FNL fighters are demanding talks on political and military power-sharing.
Bujumbura insists there is nothing more to talk about.
The UN Security Council expressed serious concern about the recent fighting on Thursday.
It threatened possible sanctions against those it said were jeopardising the peace process.
The council unanimously approved a statement that "condemns the use of violence" and urged the government and the FNL "to scrupulously respect the ceasefire" agreed on September 2006.
The Council urged both sides to resume their dialogue to overcome obstacles hindering implementation of the ceasefire agreement.
The 15-member council said that "any attempt to jeopardise peace in Burundi through violent means is unacceptable", and said it was considering "additional measures, as appropriate, in support of peace and stability in Burundi".
Burundi, one of the world's poorest nations, is still trying to overcome the legacy of its 1994-2006 civil war.
At least 300,000 people died during the 12-year conflict.
Since independence in 1961, the country has been plagued by tensions between the dominant Tutsi minority and the Hutu majority.