By Sunday afternoon, about 580 foreigners had been evacuated from Ndjamena and taken to neighbouring Gabon, French military officials said.
France, the former colonial ruler of the central African nation, has reaffirmed its support for Deby's government and offered to help him leave the country, an offer he has so far rejected.
"Instead of evacuating him and rapidly establishing relations with us, France persists in backing Deby," Timane Erdimi, a rebel leader, said in an interview with the French newspaper Journal du Dimanche.
The conflict has left France walking a tightrope as it tries to salvage a European peacekeeping mission for Darfur refugees and prevent its forces from being drawn into combat in Chad.
Bernard Kouchner, the French foreign minister, while condemning a "brutal attack on a legal government, against an elected president" has made it clear the 1,450 French troops would not get involved.
French forces are in Chad
to provide logistical and intelligence support to Deby's government and Paris sent an extra 150 soldiers to help evacuate foreign nationals.
But the French military has been drawn into fighting in Chad in the past: in 2006, it helped fight off another rebel assault on Ndjamena, to the anger of Deby's opponents.
The violence has already caused the suspension of a planned European peacekeeping force (Eufor) deployment to Chad and neighbouring Central African Republic, now put back to Wednesday.
"Nobody has the intention of giving up this operation," Herve Morin, the French defence minister, said of the Eufor deployment, championed by France to protect refugees from Sudan's Darfur province just over the border.
The Chadian foreign minister accused Sudan of masterminding the rebel offensive in a bid to halt the Eufor deployment.
"Sudan has sent these attackers more than 700km to destroy out capital," Allami said, speaking in Addis Ababa, Ethiopia.
|The government says fighting is over but rebels |
say they are only letting foreigners leave [AFP]
General Mahamat Ali Abdallah Nassour, a Chadian military commander, said Sudan's troops had joined rebels in attacking the town of Adre, on the border with Sudan's Darfur region, calling it "a declaration of war".
The rebels reported to have surrounded Adre are not part of the three-group rebel alliance that entered the capital on Saturday, but Ahmat Soubiane, their leader, said his forces were "acting in co-ordination with the rebels in Ndjamena".
"All our organisations have a single goal - the departure of Idriss Deby," he said.
Khartoum on Sunday denied any involvement in the fighting in Chad, but Kouchner told the Journal du Dimanche newspaper that it was absolutely certain that these Chadian [rebel] forces come from Sudan".
Paris fears that a foothold in Chad would enable Khartoum to further undermine international efforts to end the Darfur conflict, and hopes a negotiated settlement could prevent Sudan from extending its influence in Chad.
Foreign and local residents said heavy weapons and machine-gun fire erupted before dawn on Sunday near the presidential palace to the west of Ndjamena, located on the banks of the Chari river.
The main market and the national radio station were destroyed by fires and looting, witnesses said.
While no detailed casualty figures were immediately available, Radio France International quoted the medical charity Medecins Sans Frontieres (MSF) as estimating that several hundred people had been injured in last two days of confused street fighting.
One resident told Al Jazeera that he had seen bodies in the streets.
"And I saw cars burning, during the night and all day ... there was heavy shelling over our heads," Fayez el-Fadl, a restaurant owner in Ndjamena, said.
Haru Mutasa, Al Jazeera's correspondent in Chad, reported that a lot of people were stuck in their homes, too scared to leave in case they are caught in the crossfire.
About 400 people had fled across the western border into Cameroon, according to the UN refugee agency.
Source: Al Jazeera and agencies