Sudan and Chad have previously fallen out over alleged support for rebels
Chad's government says the army has killed 105 insurgents and beaten back a new attack near the Sudan border, but the rebels have denied the claims.
FPRN leader Adoum Yacoub said both sides had lost lives but did not give any details.
This is the first battle since Chad and Sudan agreed to stop supporting rebels in each other's country in February.
Chad's President Idriss Deby this week sent a message congratulating Sudan's Omar al-Bashir on his re-election.
"Our security forces... completely control the entire zone," said Chad's Information Minister Kedallah Younous, admitting that one soldier had been killed and eight wounded.
There are no independent reports from the area, which borders Sudan's volatile Darfur region.
Former BBC Chad correspondent Celeste Hicks says it is unlikely that the FPRN rebels could make serious inroads without backing from Sudan.
It is a new group, which broke away from the main UFR formation because it was opposed to peace talks with the government, she says.
As part of the February deal, Chad and Sudan agreed to set up a joint force to patrol the border and Chad has not said it is pulling out of this agreement.
Sudan has long accused Chad of backing rebels in Darfur, while in 2008, Chad said Sudanese had helped a rebel group which almost reached its capital, N'Djamena, before being beaten back.
This led to Chad breaking diplomatic relations with its neighbour.