The UN says Sudan and Chad are fighting a proxy war through rebels
Rebels in Chad say they have taken the eastern town of Biltine - the third town they have captured in recent days.
They say they will march to N'Djamena, 750km (470 miles) away, to oust President Idriss Deby. There was no immediate reaction from Chad's capital.
Mr Deby accused the EU force in Chad (Eufor) of "turning a blind eye" to the killings of civilians by the rebels.
Separately, the UN refugee agency said it had halted activities in eastern Chad due the deteriorating security.
The UN High Commission for Refugees (UNHCR) said the town of Abeche, the agency's main operating base in the east, "was sealed off by the Chadian National Army on Monday, making movement very difficult".
There are 12 refugee camps in eastern Chad housing some 250,000 refugees from the conflict-torn Darfur region in neighbouring Sudan.
A spokesman for the rebel National Alliance said on Monday that the attackers had met no resistance in Biltine.
They were not planning to remain in the town, he said. The rebels only briefly occupied Goz Beida and passed through Am Dam.
There was no immediate reaction from the government or independent confirmation that Biltine had fallen.
The government described a previous claim of a rebel advance as a "publicity stunt".
It said on Sunday that the rebels were trying to draw security forces out of their defensive positions in towns and cities.
On Monday, President Deby accused the Eufor of failing to prevent the killings of civilians and refugees by the rebels.
"We have the right to ask ourselves about the effectiveness of such a force, of the usefulness of its presence in Chad," he said.
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, 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.