A group of Sudanese militia has crossed into Chad, attacking villages in the east of the country and killing 36 people, says the government in Chad.
The Darfur conflict has caused some 2m to flee
The government says the men, who were in uniform and on horseback, were trying to steal cattle.
The Chadian army is reported to have killed seven of the attackers.
The attack is reported to have taken place on Monday close to the Sudanese border and follows reports of clashes between armed men the week before.
An Arab militia - the Janjaweed - has been accused of carrying out cross-border raids in the past.
They have been armed and supported by Sudanese government forces, western officials say, although the government denies this.
On Monday, a senior United Nations official said Sudan's government had done little to disarm or reign in the Janjaweed in the western province of Darfur, which borders Chad.
He said a culture of impunity existed there.
At least 200,000 Sudanese have crossed the border into Chad from violence in Darfur during the two-and-a-half-year conflict.
Two million have fled their homes but remain inside Sudan.
The last few weeks have seen the resumption of Darfur's peace talks in Nigeria but also an escalation in fighting.