"We have taken the decision to break our diplomatic relations with Sudan today and to proceed to close our frontiers," he told a rally in N'Djamena on Friday.
Chad's government has repeatedly accused its western neighbour Sudan of financing and arming anti-Deby rebels from the conflict-torn Sudanese region of Darfur.
Deby also warned that his country could stop sheltering thousands of Sudanese refugees that have fled the embattled Darfur region.
Neighbour Central Africa closed
its border with Sudan on Friday
In a related move, the Central African Republic closed its border with Sudan on Friday in protest against what it called Khartoum's "aggression" following rebel attacks on its neighbour Chad, its foreign minister, Jean-Paul Ngoupande said.
Chadian rebels attacked the capital N'Djamena early on Thursday in the boldest assault yet by fighters who have pledged to end Deby's nearly 16-year rule and block a May 3 presidential election in which he is standing for re-election.
Sudan responded by saying it would expel Chad's ambassador.
"The foreign ministry has decided to expel the Chadian ambassador to Sudan as a reaction to the accusations and aggressions by Chad on Sudan," said a statement on Sudan's official Sudan News Agency.
The Sudanese government also denied it was helping anti-Deby rebels. "Let me repeat that Sudan is not involved in these Chadian internal affairs. They have a revolt," said a foreign ministry spokesman, Jamal Ibrahim.
Washington said Chad's move would only exacerbate tensions as it urged the country and other African nations to work for an end to the violence.
"Let me repeat that Sudan is not involved in these Chadian internal affairs. They have a revolt"
Sudan's foreign ministry spokesman
"Things have heated up to a point where we have seen violence get out of hand, and it is incumbent upon all parties to do what they can to provide security to reduce those levels of violence, as well as to make sure that all international obligations that they have are lived up to," said the State Department's spokesman, Sean McCormack.
Washington has "grave concerns" about Chad sealing off its borders with Sudan and the impact on refugees as well as access to camps on both sides of the border, McCormack said.
"So we call upon the government of Chad to uphold its responsibilities, as outlined by the UN and international obligations, to provide protection for these refugees as well as to provide international access to the refugees."
Deby had criticised the international community for being slow to react to the border crisis with Sudan, a spillover from the Darfur conflict where pro-Khartoum Arab militias battle other ethnic groups.
"If after June, we can't guarantee the security of our citizens and the refugees, then it is up to the international community to find another country for these refugees," he said.
Chadian government forces on Thursday repulsed an attack in which at least 350 people died and 271 rebels were captured, the country's territorial management minister said on Friday, adding that the rebel force was completely destroyed.
General Mahamet Ali Abdullah the dead included government troops, rebel forces and civilians caught in the fighting. He said the army also captured 14 pickups used by the rebels.
Chadian troops paraded the prisoners and laid out the bodies of dead insurgents at the National Assembly building on Friday.
Some of the rebels spoke of being conscripted in the rebel United Front for Change (FUC). Others said their commanders told them they would not meet any resistance when they attacked N'djamena before dawn on Thursday.
In just three days, the rebels charged 1,000km in pickups from their bases and came close to capturing the National Assembly building in the centre of the capital, N'djamena.
Government troops pushed them back with tanks, artillery and attack helicopters.
Deby first presented the prisoners to the media on Thursday evening. Four tanks guarded the presidential palace on Friday.
French military aircraft in Chad transported Chadian soldiers to the country's southeast, on Thursday and Friday, the French defence ministry said.
A C-160 aircraft carried about 40 soldiers from N'Djamena to Sahr, 500km to the southeast and around 100km from the Central African border, following a Chadian request.
France said its troops in Chad are
not engaged in fighting rebels
The plane was also carrying light weapons, the Defence Ministry said, adding that the flight was considered to be "logistical support", provided under a military co-operation agreement linking France and Chad.
France, which ordered 150 troop reinforcements to Chad on Wednesday in response to the worsening security situation, has said its 1,200 soldiers based in the country are not involved in fighting the rebels.
The ministry said the operation was intended to prevent a possible offensive by rebel forces seeking to topple Deby's government.
On Thursday, a leader of the rebel FUC said that French fighter planes had bombed rebel-held towns in eastern Chad, a charge dismissed by the French authorities as "without foundation".