Burundian officials and witnesses said the armed group crossed into Cibitoke province north of the capital Bujumbura during the night, but that Burundian soldiers and police had managed to gain the upper hand after a day of fighting.
"The fighting has just come to an end. I myself counted 14 bodies of attackers who were killed in the fighting," the governor of Cibitoke province, Anselme Nsabimana, told AFP.
He said security forces had prevented the group from reaching the Kibira forest, an area used in the past as a base to stage further attacks inside Burundi.
"Our soldiers are pursuing them. Roadblocks have been put up so that they don't escape," he said, adding that reinforcements had been sent to the area.
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A local witness said around 200 fighters armed with assault rifles and grenade launchers crossed into the country from DRCongo's eastern Kivu region, a chronically unstable and resource-rich area that is home to dozens of rebel groups.
Fighting has been concentrated around Buganda, situated 50 kilometres (30 miles) north of the capital Bujumbura, and officials said thousands of residents had fled the area.
The main body of FNL -- a highly disciplined group notorious for singing hymns as they carried out attacks -- signed a peace deal with the Burundian government in 2009 and have since become a political party.
The rebels who still fight on have claimed a string of attacks this year, most recently in October when they claimed to have killed six soldiers, and vowed to "intensify" their raids ahead of presidential elections in June 2015.
Burundi, a small nation in Africa's Great Lakes region, emerged in 2006 from a brutal 13-year civil war and its political climate remains fractious ahead of the polls.
President Pierre Nkurunziza, in power since 2005, is expected to run for a third term in office next year despite opponents' claims that that would violate Burundi's constitution.