The UN says Sudan and Chad have been fighting a proxy war
The Chadian government has accused Sudan's army of attacking a town on their border after days of rebel raids.
Communications Minister Mahamat Hissene told the BBC that the garrison town of Ade had been attacked by ground troops supported by helicopters.
Mr Hissene said the fighting was continuing and confirmed a rebel raid on the smaller town of Am Zoer.
Last month, Sudan accused Chad of helping a Darfur rebel group attack a city just outside the Sudanese capital.
Chad denied the allegation but the UN says Sudan and Chad have been fighting a proxy war through each other's rebel groups.
The two countries have signed numerous peace deals but these have never held.
In February, Chadian rebels reached President Idris Deby's palace before being repelled by government forces.
In recent days, the rebels have attacked several towns in the east, briefly occupied them, and then moved on.
They say their intention is to march hundreds of kilometres to N'Djamena to oust President Deby.
Mr Hissene told the BBC's French Service that Sudan was revealing "its true colours" by attacking Ade.
"There were Sudanese army helicopters, backing up Sudanese troops that had already been massed on the ground for several days," he said.
In a statement the government said its reaction would be "on a level with the impudence of the Sudanese regime", Reuters news agency reports.
Regional analyst Alex de Waal says he thinks the countries are on the brink of an "international war".
"After the Darfur rebel group attacked Khartoum, the Khartoum government said it saw the fingerprints of the Chadians all over the operation," he told the BBC's World Today programme.
"They resolved that they would not rest until they had overthrown the government in Chad and I think what we're seeing is part of that operation."
There are 12 refugee camps in eastern Chad housing some 250,000 refugees from the conflict-torn Darfur region in neighbouring Sudan.
On Monday, the UN refugee agency said Abeche, its main operating base in the east, had been sealed off by the army.
Earlier, President Deby accused the European peace force, which operates in eastern Chad, Eufor, of co-operating with rebels as they continue their latest offensive.
"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," the president said in a televised address.
"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.
Mr de Waal says Mr Deby has done his utmost to make Eufor into a defence force against the rebels.
"The European Union force in Chad has been caught in a bit of a trap - most of the troop contributing countries do not want to get involved in a shooting war; they don't want to be partisan.
"Trying to keep the peace when there's no peace to keep is actually an impossible mandate, so the European Union troops have essentially decided to keep their heads down and stay out of the war as it begins to unfold."
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