Deby wore a military uniform as he talked to reporters in the presidential palace, making his first public comments since rebels attacked the capital of Ndjamena.
The fighting left at least 100 civilians dead and sent about 20,000 fleeing into Cameroon and Nigeria, according to media reports. Some have started to return home.
"We are in total control, not only of the capital, but of all the country," Deby said.
Earlier in the day, he met with French Defense Minister Herve Morin, who traveled to Chad in a show of support for its former colony, where it has warplanes and more than 1,000 troops stationed.
At stake in Chad is control of a central African country with promising oil reserves but a porous border with Sudan's remote and troubled Darfur region.
Chad has accused Sudan of backing the rebels to prevent deployment of an international peacekeeping force to protect refugees from Darfur. Sudan has long resisted such a force, but has denied involvement in the coup attempt.
On Wednesday, Chadian Prime Minister Delwa Kassire Coumakoye also alleged that Libya was involved in supporting the rebels.
"It is Gaddafi who is contributing to arming these people," he said, referring to Libyan leader Moammar Gaddafi. "They are armed by Sudan and supported by Libya."
Deby later downplayed any differences with Libya, saying relations are "excellent" between the countries.
France initially said it was "neutral" as fighting raged over the weekend, but later threw its weight behind Deby.
The bodies of at least 100 civilians lay in Ndjamena's three main hospitals and as many as 700 more people were being treated for bullet wounds and injuries from mortar fire, Guilhem Molinie, a Doctors Without Borders official, told Reuters. He said the death toll was likely to rise as Red Cross workers were still recovering bodies.
Chadian Red Cross officials have said hundreds of civilians were killed in the fighting, but no official death toll has been given.
On Wednesday, more people were reported to be returning to Ndjamena than leaving across two bridges spanning the Chari.
A Chadian police officer with a megaphone told the crowd at the border: "Come back home. Ndjamena is at peace," Agence France-Presse reported.
An Associated Press reporter saw small groups of men heading toward Ndjamena, about 40 in an hour. Many said they left wives and children in Cameroon while they returned to protect their houses from looters and assess the security situation in the capital.
Most shops and buildings in downtown Ndjamena have been looted. Outside the city center, the state broadcasting station and the parliament building were stripped.
Deby told reporters that the Chadian army was chasing the rebels, who were fleeing east. "We are going to catch them before they enter Sudan," he said, speaking for about 30 minutes while seated in a chair in front of the flags of Chad and the African Union.
But he suggested his government had been weakened.
"I am working with less than a quarter of the members of my government," he said. "I do not know where the rest have gone."
"There are traitors. When the time comes we shall work on that issue," he added.
The rebels accuse Deby of corruption and embezzling millions in oil revenue. While many Chadians may share that assessment, the uprising appears to be a power struggle within the elite that has long controlled Chad; rebellion leaders include Mahamat Nouri, a former defense minister, and Timan Erdimi, a nephew of Deby who was his chief of staff.
The U.N. Security Council has condemned the attack and authorized France, which has given Deby strong support in the past, and other nations to help Chad's government.
French President Nicolas Sarkozy said French troops were ready to attack the rebels if necessary, though his government has stressed no such plans were imminent.
Morin suggested the rebels were not completely routed, telling France-Inter radio that his intelligence showed a column of insurgent reinforcements was moving in. French officials had said earlier that 100-200 rebel vehicles appeared to have regrouped east of the capital.
Rebel spokesman Abderaman Koulamallah said the insurgents had pulled back "to better camouflage themselves" about 45 miles from the capital.
"We warn France against all direct intervention otherwise things could very badly degenerate for it," he told AFP by satellite telephone. "It would risk losing face in Chad and endanger the lives of all its nationals in Africa."
On Friday, rebels attacked Ndjamena in pickup trucks after advancing in a matter of days from their eastern bases near the border with Sudan. The fighting left bodies in downtown streets. The rebels withdrew late Sunday, and by Wednesday morning the city was quiet, the streets almost empty.
Chadian health officials pleaded for doctors and nurses to return to N'Djamena to help the wounded.
The U.N. World Food Program has said its food deliveries to more than 420,000 people are threatened by the violence.
In light of the French help, Deby said he would consider pardoning a group of French charity workers sentenced to eight years in prison on kidnapping charges for trying to fly children they claimed where Darfur orphans out of Chad.
