It said Janjaweed militias, accused of atrocities against civilians in the neighbouring Sudanese region of Darfur, backed by mercenaries, attacked in the area of Moudeina.
In N'Djamena, the foreign ministry said: "The Chadian national army bravely repulsed this new aggression, which constitutes a flagrant violation by the Khartoum government of the Tripoli agreements of February 8, 2006.
"Chad condemns this aggression and will draw the necessary consequences," it said, without detailing what these might be.
Ahmat Allami, the foreign minister, said that the "mercenaries" were in fact rebels from the Rally for Democracy and Liberty (RDL), which Chad accuses Sudan of arming and backing.
Military sources in N'Djamena said heavy fighting was continuing several hours after the initial attack.
Chad and Sudan signed a peace deal on February 8 under the aegis of Libya and the African Union agreeing they would not harbour rebels on their territories or conduct mutually hostile activities.
Idriss Deby condemned Sudan's
'financial' backing of rebels
The agreement put an end to a months-long row during which the two countries traded accusations of destablisation attempts.
The tensions reached a peak in December after RDL rebels attacked the Chadian town of Adre, an act Chad blamed on Sudan before declaring that it was in a "state of hostility" with its eastern neighbour.
Earlier this month Chad again denounced incursions by "Sudanese militias" into its territory, and last week Idriss Deby Itno, the president, again condemned Sudan's "material and financial" backing for the rebels on its land.
"Sudan has fulfilled none of its promises, neither disarming the Janjaweed, nor disarming the Chadian rebels. We wonder about the validity of the declarations made in Tripoli," Ahmat Allami said.
He claimed between 4,000 and 5,000 Chadians living in frontier villages had fled their homes to seek shelter from the Janjaweed horsemen.
Humanitarian organisations say about 30,000 Chadians have been displaced since the end of December by cross-border attacks in the east of the country, where some 200,000 Sudanese refugees have sought safety after fleeing Darfur.