Deby, speaking at the presidential palace on Saturday, said: "The government must re-evaluate relations between Sudan and Chad, and envisages - if the situation does not evolve positively - the rupture of these relations.
"To this end, Sudanese cultural centres must be closed and schools financed by Sudan must be taken over by the Chadian government. Teachers who are really intelligence agents ought to return home."
Deby himself took power in a putsch launched from Sudan in 1990. Khartoum rejects the accusations of involvement with the UFR.
South of Abeche, in the town of Am-Dam, government forces showed off their booty and prisoners to journalists, who also saw dozens of bodies and burned-out vehicles.
But a UFR source claimed that their forces were still massed southeast of Abeche and are intent on taking the capital, at least 600km to the west.
Adam Mustafa Ibrahim, the governor of Abeche, told Al Jazeera: "Security forces are on alert; they are patrolling the borders and control the situation.
"We do not pay attention to rumours, but if there is solid information regarding rebel movements, we will attack them as we have before."
The fighting looks to have ended a peace accord signed by Khartoum and Ndjamena two weeks ago - the latest in a series of deals, none of which has had any longevity.
The UN security council on Friday condemned the UFR incursion into eastern Chad from Sudan.
All 15 ambassadors agreed to a non-binding statement that "condemns the renewed military incursions in eastern Chad of Chadian armed groups, coming from outside".
The UN statement also stressed that "any attempt at destabilisation of Chad by force is unacceptable".
The European Union (EU) and African Union (AU) have spoken out against the UFR offensive.
Javier Solana, the EU foreign policy chief, called on "the armed groups coming from Sudan in the east of Chad ... to renounce violence and begin negotiations with the Chad government."
Meanwhile, Ramtane Lamara, the AU's peace and security commissioner, condemned "all kinds of anti-constitutional change of government, and acts of destabilisation".
Chadian opposition fighters have sought to overthrow Deby for more than three years.
The UFR is led by Tiimane Erdimi, Deby's nephew, who once held the brief of oil affairs in the government.
However, a split occurred within Deby's inner circle over how to deal with the conflict in Darfur in Sudan leading to the rebellion.
Deby and many of his senior military officers hail from Sudan and have relatives living in Darfur.
About 300,000 Darfuri war refugees are camped in eastern Chad along with about 187,000 Chadians who have been uprooted by fighting in Chad and Darfur.