- The incursion happened at around 18:00 on Sunday, the day of the country's presidential election.
- The rebels have since been chased and dispersed by armed forces, according to a statement by the government.
- Preliminary election results will not be announced until 25 April.
The situation in northern Chad is now "completely under control" after rebels entered the area on Sunday, the day of the country's presidential election, the government said.
The incursion by "several columns of heavily armed vehicles coming from Libya" happened at around 18:00 on Sunday in the Zouarke area in Tibesti province, around 1 000 kilometres (600 miles) north of the capital N'Djamena, government spokesman Cherif Mahamat Zene said in a statement.
But the rebels were chased and dispersed by the armed forces and "the government now assures the public that the situation is entirely under control," according to the statement released late Monday.
The Tibesti mountains near the Libyan frontier frequently see fighting between rebels and the army, and French air strikes were needed to stop an incursion there in early 2019.
In February 2008, a rebel assault reached the gates of the presidential palace before being pushed back with French backing.
Already on Monday, army spokesman Azem Bermandoa Agouna had said that "steps have been taken to neutralise" the incursion.
But the FACT group, mostly made up of Saharan Goran people, said its forces had taken "without resistance" garrisons including Wour and Zouarke, near Chad's borders with Niger and Libya.
Based in Libya where it has a non-aggression pact with Khalifa Haftar, the military strongman of the country's east, FACT emerged in 2016 when the UFDD group that led the 2008 offensive split.
Its leader Mahamat Mahdi Ali called on Chadians to "keep up pressure on the dictatorship" and "help FACT fighters free the homeland".
The incursion came on the same day as 30-year President Idriss Deby Itno was expected to win re-election.
Although vote-counting was finished in polling stations on Monday, preliminary results will not be announced until 25 April after a drawn-out compilation process.
Initial indications suggested large numbers of people stayed away from the vote, prompting opposition figures to claim their calls for a boycott of the polls had worked.