French warplanes on Sunday struck twice to halt an armed group that crossed into northern Chad from Libya in a column of 40 pickup trucks, the French military said, adding it acted at Chad's request.
A rebel group opposed to President Idriss Deby said it had been the target of the strikes, and warned France that its act could stir "hostility towards the French."
In a statement on Monday, the French military said that Mirage 2000 fighters intervened "together with the Chadian army" to "halt the hostile advance and disperse the column," which had crossed deep into Chadian territory.
The warplanes are based near N'Djamena, the Chadian capital, as part of France's Barkhane counter-terrorism force in the Sahel.
"The column had been spotted at least 48 hours beforehand," armed forces spokesman Patrik Steiger told AFP.
The Chadian airforce carried out strikes to try to repel it before asking the French to intervene, he said.
On Sunday morning, French planes made low warning passes over the column but it continued to advance, triggering a decision to scramble more fighters, which carried out two strikes at around 6:00 pm Paris time.
Steiger said the group had crossed 400 kilometres (250 miles) of Chadian territory before being halted "between Tibesti and Ennedi" in the northwest.
He did not identify which armed group they belonged to.
But the spokesman for Chad's most active rebel group, the Union of Resistance Forces (UFR), said that the raid had targeted its men.
Reached by AFP from the Gabonese capital Libreville, UFR spokesman Youssouf Hamid said the strikes marked a "dangerous turn" by France in Chad's "internal affairs."
"The Chadian people will respond. It may take the form of showing hostility towards the French," Hamid said.
"Paris has become a force that is hostile to the Chadian people," he added.
Hamid did not give any details about the objective of the incursion.
The UFR was created in January 2009 from an alliance of eight rebel groups.
In February 2008, a tripartite insurgent group, moving in from the east, reached the gates of the presidential palace in N'Djamena before being repulsed by Deby's forces.
Deby accused Sudan of supporting the attack, a charge that it denied.
In a separate development, forces loyal to Libyan strongman Khalifa Haftar said on Monday they carried out air strikes at the weekend against Chadian rebels in southern Libya.
"Chadian mercenaries suffered heavy losses of men and equipment" in the Murzouk region in the operation on Sunday, said a spokesman for Haftar's self-styled Libyan National Army.
It was not possible to confirm the report, and it was unclear if Sunday's operation was linked to the French air strikes.
Chad, a vast and mostly desert country with more than 200 ethnic groups, has suffered repeated coups and crises since it gained independence from France in 1960.
Deby, a former head of the armed forces, became president of Chad in 1990 after ousting his former boss, Hissene Habre.
Under his presidency, the country has become a leading member in the fight against jihadism in the Sahel. It is part of the West African coalition fighting Boko Haram and a member of the French-backed G5 Sahel anti-terror alliance, which also includes Burkina Faso, Mali, Mauritania and Niger.
The latest incursion follows several recent air strikes by the Chadian air force against Libya-based rebels in the far north.
It also launched an operation last year aimed at "clearing out" illegal gold miners whose arrival in the region has fomented unrest with locals.