“The situation in N’Djamena is under the control of the defence and security forces,” Deby told French radio RFI.
He added that a planned presidential election would go ahead in the country as scheduled on May 3.
Residents and diplomats earlier said Chad government forces fought rebels in N’Djamena after a column of insurgents had penetrated the northeast of the city, according to a Reuters report.
Residents said the fighting appeared to be taking place in the northeast of the capital where the national parliament and a Libyan-run hotel complex are situated.
“They (the rebels) are in the city,” a Reuters reporter said, as the sound of artillery and machinegun fire could be heard coming from the northeast sector where the national parliament is located.
“It can be heard from within the city, artillery and machinegun fire,” the reporter said. Rebels are said to be working to overthrow President Idriss Deby.
Both the United Nations and the US embassy were planning to evacuate non-essential staff when the situation allowed, diplomats said.
One resident reported seeing a column of smoke. Most people were staying indoors and there was little traffic.
“I’m sitting here listening to the boom-boom,” one foreign resident, who asked not to be named, said.
Residents had been woken by the sound of heavy weapons but said the fighting appeared to be moving closer and bursts of machinegun fire could also be clearly heard.
N’Djamena went on the alert on Wednesday as rebels advanced closer to the capital of the landlocked central African oil producer after a wave of hit-and-run attacks over the last three days.
Diplomats earlier said the insurgents had moved to within 40 kilometres of the capital but were meeting stiff resistance from government forces.