Chad's president has accused the European Union's protection force, Eufor, of co-operating with rebels as they continue their latest offensive.
Idriss Deby said on Chad TV that Eufor was allowing rebels to steal fuel, food and vehicles from humanitarian workers.
Hours after he spoke the rebels said they had captured a fourth town, Am Zoer, 70km (40 miles) from Abeche.
On Monday, the UN refugee agency said Abeche, its main operating base in the east, had been sealed off by the army.
Meanwhile, the United States moved all non-emergency staff from its embassy in the Chadian capital, N'Djamena, to Cameroon.
UN Secretary General Ban Ki-Moon and the UN Security Council have both condemned the rebels' actions.
There are 12 refugee camps in eastern Chad housing some 250,000 refugees from the conflict-torn Darfur region in neighbouring Sudan.
Proxy war
"We have taken Am Zoer after violent clashes. We took prisoner a chief of the garrison," a spokesman for the National Alliance rebel group told AFP news agency.
Correspondents say in recent days the rebels tend to go into a town, briefly occupy it and then move on.
The rebels say their intention is to march to N'Djamena, 750km (470 miles) away, to oust Mr Deby.
In a televised address, President Deby accused Eufor of failing to prevent the killings of civilians and refugees by the rebels.
"We've been surprised to see that, in its first hostile test, this force has rather cooperated with the invaders, allowing humanitarian workers' vehicles to be stolen and their food and fuel stocks burned and closing its eyes before the systematic massacre of civilians and refugees," he said.
"We have the right to ask ourselves about the effectiveness of such a force, of the usefulness of its presence in Chad."
Troops in the French-dominated, 3,700-strong Eufor started to deploy to Chad and the Central African Republic in April after a brief delay caused by an attempt by rebels to overthrow the Chadian government.
In February, the rebels reached President Deby's palace before being repelled by government forces.
The UN has said Sudan and Chad are fighting a proxy war through each other's rebel groups. Last month, rebels from Sudan's Darfur province reached the outskirts of the Sudanese capital, Khartoum, before being repelled.
Sudan blamed Chad for that attack - charges denied by Mr Deby's government.
The two countries have signed numerous peace deals but these have never held.
(BBC)
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