Chad's government is worried that Sudan's Arab militia is trying to export ethnic violence from Darfur.
The Janjaweed are accused of chasing black Africans from their homes
Chad says that it killed 69 Sudanese "Janjaweed" fighters on its territory.
The pro-Sudanese government Janjaweed have been accused of carrying out ethnic cleansing against Darfur's black African population.
Some 10,000 people have been killed and more than a million have fled their homes. Chad's border region has the same ethnic make-up as Darfur.
The BBC's Abakar Saleh in the Chad capital, Ndjamena, says the authorities there are "very worried" that the Janjaweed are trying to stir up trouble amongst Chad's Arab population.
"There is a hidden force trying to export the conflict between the Sudanese into Chad," said Allami Ahmat, diplomatic advisor to Chadian President Idriss Deby.
The Janjaweed were killed after attacking the village of Birak, some 6km inside Chad's territory, said Communications Minister Mouckhtar Wawa Dahab.
He said that two militiamen were captured but had no information on Chad casualties.
Our correspondent says that President Deby is himself from the Zagawa group which straddles the border and which is being targeted in Darfur.
The Arabs are one of Chad's biggest groups but do not control the government as in Sudan, he says.
Aid workers describe Darfur as the world's worst humanitarian crisis.
But United Nations Secretary General Kofi Annan says it is not the "genocide", which some human rights groups have called it.
They say they are in a "race against time" to get aid to those who have fled their homes in Darfur before the rainy season makes the areas impassable.
President Deby has ethnic ties to those being targeted in Chad
The first rains have already started to fall and the BBC's Hilary Andersson says that some children in camps for the displaced are starving to death because there is not enough food aid.
Chad has been trying to mediate between the Darfur rebels and the government.
A ceasefire was signed in Ndjamena but both sides accuse the other of breaking it.