In military uniform, Deby said at a news conference on Wednesday that government troops had won a "stunning victory" over opposition forces.
Deby said that most of the fighters had come from Sudan, with very few Chadians involved in the uprising.
Rebels disguised as civilians'
He said there were "rebels who have fled, there are some still in Ndjamena disguised as civilians, there are some trying to get back to the border" with Sudan.
"We're at their heels and we shall catch them before they get back to Sudan," he said, adding that Chad was "attacked from abroad".
Haru Mutasa, Al Jazeera's correspondent in Ndjamena, said that Deby "looked in good shape".
"He was making jokes. And he came out to give a warning to the rebels not to return.
"He doesn't call them rebels, he calls them mercenaries. And he vowed to deal with each one of them should they return to the capital."
Morin was also due to meet French forces stationed in Chad later in the day. There are more than 1,900 French soldiers with fighter jets in what is a former French colony.
Corpses in the streets
Battles between troops and rebels on Saturday and Sunday left bodies strewn in the streets and forced many to flee Ndjamena.
Morin said that alliance reinforcements were now coming closer to the city, albeit slowly.
Al Jazeera spoke to Guilhem Molinie, in Ndjamena working for the international aid group Medecins Sans Frontieres (MSF), who said: "The people inside Ndjamena think that rebels are still around the capital.
"Most people are suffering from bullet wounds and shrapnel impacts."
Molinie added that the coming days would be difficult for the people, even if the rebels did not return: "There are big queues in front of the bakers and at the markets."
The opposition forces are attempting to end Deby's 18-year rule in the central African nation.
The UN on Monday condemned the attacks and authorised countries to assist Deby's government.
Sarkozy said on Tuesday that France would support the Chadian government militarily if necessary.
Deby's government refused a ceasefire with its opponents on Tuesday, saying it was not needed as the rebels had been "decimated". An alliance spokesman had offered an end to the fighting if the president stepped down.
Suspected Sudanese support
Khartoum denies Chad's claim that the fighters are Sudanese and supported by the Sudanese government.
Mutasa said relations between the two countries were strained: "It has brought up old wounds with Sudan, with each previously accusing the other of funding rebel groups to destabilise each country."
By Tuesday evening the capital's streets were deserted.
The government made radio broadcasts saying it had expelled all rebels in the city and appealed for residents to return.
However, Bernard Kouchner, the French foreign minister, said on French radio on Wednesday that rebels seemed to be regrouping outside Ndjamena.
"For the moment, it is President Deby who holds the capital, but 100 or 200 [rebel] vehicles appear to have regrouped east of Ndjamena," he said.
French warplanes have been flying reconnaissance missions over opposition positions.
In the same broadcast Avocksouma Djona, the Chadian health minister, appealed to doctors and nurses to return to Ndjamena to treat the injured.
Mutasa confirmed that Chadian police officers were now at the border with Cameroon urging people to return to the capital, but people still feared more fighting there.
"The rebel groups have only agreed to some kind of cease fire, they have not admitted defeat yet as far as people in Ndjamena are concerned.
"And they think that all the rebels are waiting to do is regroup and come back. It is thought that some have merged into the civilian population and others are hiding in remote villages in Chad."
A death toll for the fighting has not been given, but the International Red Cross has said that more than 1,000 people, including many civilians, have been injured.
President Idriss Deby seized power in a Libyan-backed coup in 1990
He went on to win the Chad's first two
multi-party elections in 1996 and 2001
A ceasefire signed between Deby and four rebel groups in October recently collapsed
The largest rebel group, the Union of Forces for Democracy and Development, is led by a former minister who accuses Deby of corruption
Click here for more on Chad's spiral into conflict
The UN refugee agency has said that up to 20,000 locals have fled to neighbouring Cameroon.
More than 1,000 foreigners, many French, have been evacuated from the oil-rich country, and those remaining are reportedly camped in hotels guarded by French soldiers with armoured vehicles.
The rebels accuse Deby of corruption, misappropriation of oil revenues and running a dictatorship. Although these accusations are shared by many in the country, the fighting appears to be a struggle between national elites.
Opposition leaders include Mahamat Nouri, a former defence minister, and Timan Erdimi, former chief of staff and Deby's nephew.
No civilians or aid has been let into the country since fighting started on Friday.
Save the Children has said that aid programmes serving more than 500,000 people could dismantle if a route for emergency assistance is not opened within the next 48 hours.
Molinie said that MSF feared that seasonal illnesses in the country, such as measles and meningitis, could rise to epidemic levels if it impossible to get medicines to those in need.
"We already have measles in Gore, a town in the south where MSF works, and we are preparing for an epidemic."