Chadian forces have used tanks and helicopter gunships to try to drive back rebels besieging the presidential palace in the capital N'Djamena.
Aid agency MSF told the BBC there were "a lot of dead bodies" in the city, and 300 people being treated in hospitals.
The rebels, who want to overthrow President Idriss Deby, seized large parts of the city on Saturday.
Correspondents say the crisis could have major implications for efforts to end the conflict in Darfur.
Witnesses heard anti-tank and automatic weapons fire coming from the city centre, starting at about 0500 local time (0400 GMT) on Sunday.
French Defence Minister Herve Morin said President Deby, who is believed to be inside the palace, still had 2,000 to 3,000 men under his authority, despite rebel claims that government troops were defecting.
A spokesman for the rebels said they had also taken the eastern town of Adre, near the border with Sudan, an area where some 400,000 people displaced as a result of the conflict in Darfur are living in camps.
But the government said it had beaten back that attack, and claimed the assault had been backed by Sudanese aircraft.
June 2005 - Constitutional changes approved allowing president to stand for third term
April 2006 - Hundreds killed as rebels fight government troops on outskirts of N'Djamena
May 2006 - President Deby wins election boycotted by opposition
January 2008 - EU approves peacekeeping force to protect Darfur refugees from violence in Chad
Sudan has denied it is involved in any of the fighting in Chad.
Correspondents say Sudan is known to have supported rebels in Chad in the past - while Chad has backed rebels in the Sudanese province of Darfur.
Adre is in the area where a French-dominated EU peacekeeping force is due to deploy to protect displaced civilians and the aid workers supporting them.
Chadian officials have accused the rebels of seeking to stop the deployment of the EU force.
In other developments:
More than 500 French and other foreign citizens have been evacuated to the Gabonese capital, Libreville, with another 400 gathered in designated area in N'Djamena, awaiting airlift.
President Deby refused a French offer to evacuate him, French officials told AFP.
The French military said several of its combat planes had been moved out of N'Djamena for safety, although they had earlier been seen overflying the area.
France has a long-term military presence in Chad, one of its former colonies, giving the government intelligence and logistic support.
Mr Deby seized power in a coup in 1990, but has won three elections since then, although their legitimacy has been challenged.
The BBC's Stephanie Hancock, recently based in Chad, says the tide began to turn against him after his decision in 2005 to change the constitution to allow him to run for a third term in office.
THE REBEL COALITION
Unified Military Command includes:
Union of Forces for Democracy (UFDD) led by Mahamat Nouri
Rally of Forces for Change (RFC) led by Timane Erdimi
UFDD-Fundamental led by Abdelwahid Aboud Mackaye
Tensions with Sudan have also been heightened over the conflict in Darfur.
Sudan's government and pro-government Arab militias are accused of war crimes against the region's black African population.
Some 2m people have fled their homes, including an estimated 200,000 who have sought safety in Chad - many living in camps along the border with Sudan.
Aid agencies fear the fighting could disrupt $300m aid operation supporting millions in Chad.
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