Chadian President Idriss Deby Ito also threatened to expel around 200,000 refugees from Sudan's troubled Darfur region who are living in Chad, in retaliation for Thursday's offensive.
But the United States responded by giving Chad a strong warning against taking such action, saying it would be unacceptable, and called on Chad to uphold its international obligations to protect refugees.
Rebels from the United Front for Change (FUC) who are fighting to overthrow Deby meanwhile said N'Djamena is still within their reach, denying government claims that the uprising had been crushed.
"For the moment there is calm, but that does not mean that we are not in range of N'Djamena," FUC spokesman Abdel Maname Mahamat Khattat told Radio France Internationale.
"It is a tactical withdrawal," he said.
The rebel offensive has triggered alarm in the international community and comes just weeks ahead of presidential elections in the oil-rich but impoverished state in sub-Saharan Africa.
According to the government, around 370 rebels and 30 soldiers died in the fighting in N'Djamena, and another 150 rebels were killed in a battle at Adre, near the Sudanese border.
President Deby, who has showed slain and captured rebels to his supporters, said his troops had subdued the FUC rebels in the capital, and accused Khartoum of being behind the uprising.
"We decided at a cabinet meeting this morning to break off relations unilaterally with Sudan, which continues to arm mercenaries opposed to the Chad government," he told a crowd outside his residence.
Mr Deby said the international community has ignored his warnings that Sudan wants to topple him and will now have to find another host for refugees from the three-year conflict in Darfur, who are living in camps in eastern Chad.
Sudanese Foreign Minister Lam Akol Ajawin denied that Khartoum had backed the rebel offensive in the Chadian capital.
"We hope stability will prevail in Chad because instability adversely affects the security situation in the Sudan," he said.
The Sudanese foreign ministry said it would summon the Chadian ambassador to explain his government's decision to sever diplomatic relations.
Meanwhile, the Central African Republic said it had closed its border with Sudan in order not to "facilitate an attack against Chad from its territory".
The president of Chad is seeking a third term in the May 3 elections, but major opposition parties have pledged to boycott the vote, claiming they will be neither fair nor transparent.
Mr Deby recently survived an assassination and coup attempt, and has suffered desertions and defections from his entourage since the end of 2005.
Forces loyal to the president, identifiable by their red ribbons, patrolled N'Djamena on Friday, but there were fewer military vehicles deployed than the day before.
Businesses were open and taxis running as normal, an AFP correspondent said.
The government also said it was in control of the town of Adre in the east of the country near the border with Sudan where, according to humanitarian sources, fighting had been subdued Thursday evening.
The 15-member UN Security Council on Thursday strongly condemned the rebel offensive and urged Khartoum and N'Djamena not to conduct hostile activities against each other.
The members urged the Chadian and Sudanese governments to abide by a February 8 accord under in which they agreed not to shelter rebels on their respective territory and not to conduct hostile activities against each other.
The New York-based group Human Rights Watch said fighting on the border between Chad and Sudan could put refugees from Darfur at risk.
In a separate development, Chad said it would suspend oil production from next week unless it can recover funds that have been blocked by a British bank because of a dispute between N'Djamena and the World Bank.
Human Rights Minister Abderamane Djasnabaille said the oil supply would be turned off on April 18 if the World Bank did not restore access to Chad's Citibank account in London.
But he denied suggestions that there was any link between Chad's oil ultimatum and the clashes in N'Djamena.