"We don't just have control of the situation. There is no more rebellion. They have all been decimated. Those who remain are being pursued about 50km from the capital," Coumakoye said.
Rebel fighters said that they had withdrawn from Ndjamena to end "the suffering of the Chadian people, and in line with the peace initiatives of fraternal countries Libya and Burkina Faso".
Late on Tuesday, the Associated Press reported that Chadian soldiers had blocked two bridges that spanned the Chari river and had been used as escape routes for civilians fleeing to Cameroon.
Abderaman Koulamallah, a rebel spokesman, told the AFP news agency that "a non-exclusive national dialogue with a view to a peaceful resolution of the Chadian conflict" should follow the ceasefire.
The tripartite rebel alliance also wants to see "the installation of a truly democratic political regime" in Chad, which was a French colony prior to 1960, he said.
Coumakoye has accused the Sudanese government of being behind the attack, after the rebels crossed Chad last week from rear bases in the western Sudanese border region of Darfur.
"We say we are being attacked by Sudan because these elements who came were there in the shape of the Sudanese army," he said.
"The majority are children recruited in the madrassas (Islamic schools) who don't understand a word of Chadian. They aren't Chadians. They're the Sudanese people's army," he added.
Sudan has repeatedly rejected such allegations.
"Sudan has no interest in destabilising Chad," Sammani al-Wassila, Sudan's secretary of state for foreign affairs, said.
Meanwhile, Nicolas Sarkozy, the French president, said on Tuesday that France could intervene in Chad if necessary.
"If France has to do its duty, it will do so," Sarkozy told reporters.
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
"Now there is a legal decision taken unanimously by the Security Council, and if Chad was the victim of an aggression, France could in theory have the means to oppose such action."
In its statement on Monday, the UN Security Council said it "strongly condemns" the rebel offensive and called on UN nations to "provide support ... as requested by the government of Chad".
Ahmat Allami, Chad's foreign minister, met his French counterpart Bernard Kouchner in Paris on Tuesday and said afterwards that "the Chadians involved in this affair are mere instruments of a cause that isn't their own".
France has 1,450 troops and a number of Mirage fighter jets stationed in Chad.
Koulamallah has accused French military aircraft of causing "enormous" civilian casualties during the weekend, notably at the Liberte (Freedom) high school and Ndjamena's central market.
In Paris, Christophe Prazuck, a French military spokesman, called the allegation "absolutely baseless".
He said French troops in the capital had only "responded each time they were targeted or caught in cross-fire".Civilians wounded
No death toll has been given for the fighting, but many bodies have been seen in the dusty streets, and the aid group Medicins sans Frontieres has told of "hundreds" of civilians wounded.
In Geneva, the UN High Commissioner for Refugees said that 15,000 to 20,000 Chadians have taken refuge in Cameroon to escape fighting between rebels and government forces in Njdamena.
The figure comes from a UNHCR team that has reached the Cameroonian border town of Kousseri, 15km from the Chadian capital, Helene Caux, a spokeswoman for the UN refugee agency in Geneva, said.
"People are still coming through. It's a continuous flow," Caux said, adding that Kousseri was "completely swamped" by refugees.
More than 1,000 foreigners, many of them French nationals, have meanwhile been evacuated from Ndjamena or are awaiting flights out.
Source: Al Jazeera and agencies