Chad's government has admitted that its forces crossed the border with Sudan, where it clashed with the army.
A minister said Chadian soldiers were in "hot pursuit" of rebels who crossed the border and then came into contact with Sudanese soldiers.
Sudan has condemned the raid, saying 17 soldiers were killed and has reportedly summoned the Chad ambassador.
This is the first time the two armies have clashed after months of tension but Chad denies a deliberate attack.
Eastern Chad and Darfur have a similar ethnic make-up and the two governments have swapped charges of backing rebels.
Several peace deals have failed to ease the tension.
Meanwhile, the UN refugee agency says up to 400 people may have died in a cross-border raid into Chad last month.
Previous estimates said 65 people had died but one UNHCR official who had visited the area said the scene was "apocalyptic".
Chad had earlier denied that its troops had crossed the border.
But now government spokesman Hourmadji Moussa Doumgor said Chad's army was "surprised" to find the Sudanese army protecting the rear bases of rebels who had launched an attack from Sudan.
"The Chadian government denies the accusation that it deliberately attacked Sudanese armed forces," he said.
Sudan says Chadian troops backed by eight tanks and 100 vehicles were 2km (1.2 miles) inside Sudanese territory.
On Monday, Mr Doumgor said a convoy of 200 rebel vehicles had crossed the border. He said many rebel fighters had been killed, along with eight Chadian soldiers.
The long border area between Sudan and Chad shelters a murky and dangerous mix of armed groups, the BBC's Jonah Fisher in Khartoum says.
The UN investigation team in eastern Chad found decomposing bodies in the villages of Tiero and Marena, where hundreds of homes had been burned to the ground by Arab militias.
UNHCR spokesman Ron Redmond said the true number of deaths may never be known because the victims were buried in mass graves.
"Many who survived the initial attack - particularly those most vulnerable such as the elderly and young children - died in subsequent days from exhaustion and dehydration, often while fleeing," he said.
The conflict in Darfur has spilled over the border, forcing some 120,000 Chadians to join more than 200,000 Sudanese refugees in camps.
Sudan accuses Chad of backing Darfur's rebel groups - Chad's President Idriss Deby is from the Zaghawa community, which is one of the groups being attacked by pro-government Arab militias in Darfur.
Chad denies backing the rebels and in turn accuses Sudan of causing unrest among its Arab community - charges denied by Khartoum.
The UN has approved funding for an 11,000-strong force to be sent to stabilize the eastern border region, although Chad says it only wants a police operation, not a military one.
Photo caption
Chad soldiers