Some 400,000 refugees live in the Chad-Sudan border region.
Over the weekend, the UN said up to 12,000 Darfur refugees had fled to Chad following air strikes by the Sudanese military.
Al-Bashir denies backing the country's rebel group or supporting last week's attempt by rebel forces to overthrow Chad's president.
Ndjamena insists it was a bid by the Khartoum government to prevent deployment of a European peacekeeping force in the border region.
Meanwhile, the rebels on Monday urged the European Union not to send peacekeepers to the country, saying the French-dominated force will not be neutral.
The EU had been planning to send nearly 4,000 troops to Chad's border region with Darfur, but delayed deployment when fighting broke out in the capital.
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.
More on Chad's spiralling conflict...
The opposition fighters claim France, Chad's former colonial power, directly helped Idriss Deby, the Chadian president, to beat off their attack on Ndjamena.
France is contributing more than half of the 3,700-strong EU force (Eufor).
"France has shown to the world she is no longer neutral in this conflict that opposes Deby's dictatorial regime against the armed national resistance," a statement from the rebels said.
The alliance of anti-Deby groups says that French tanks and helicopters - part of a French military contingent stationed in the country - had opened fire in the recent fighting, killing civilians.
France, which has rallied international support behind Deby, denies its forces took any direct part in combat, although it said they fired back in self-defence while helping more than 1,000 French and other foreign nationals leave Ndjamena.
Eufor insists its forces will remain strictly neutral in Chad's internal conflict.
But the rebel alliance said France's "unconditional support" for Deby, whose opponents denounce him as a corrupt and dictatorial ruler, meant Eufor could not be neutral and had changed the circumstances of the deployment.
After withdrawing from the capital a week ago following battles that killed at least 165 people and injured more than 800, the rebels have moved back towards the border with Sudan.
The rebels said on Sunday they had seized the eastern town of Am Timan and that they were still in control of the centre of the country.
Since the fighting, French warplanes have been flying daily reconnaissance missions over Chad.
Pascal le Testu, a French military spokesman, confirmed that the rebels were at Am Timan.
But he said government forces controlled the central towns of Mongo and Bitkine, which the rebels claimed to have taken at the weekend.