Sudan says its armed forces have clashed with the Chadian army in the western region of Darfur, with 17 of its soldiers killed and 40 injured.
Chad shares a long border with Sudan's lawless Darfur region
Chad has denied crossing the border and says it only fought with Chadian rebels who launched an attack from Sudan.
Eastern Chad and Darfur have a similar ethnic make-up and the two governments have swapped charges of backing rebels.
A BBC correspondent says if army troops have clashed directly, it could signal a marked escalation in the conflict.
Chad shares a long border with Sudan's lawless Darfur region, where some 200,000 people have died during a four-year conflict.
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".
Sudan says Chadian troops backed by eight tanks and 100 vehicles were 2km (1.2 miles) inside Sudanese territory.
Earlier, Chad says it repelled a rebel raid launched from Darfur.
"A column of more than 200 vehicles with armed elements attacked a defence and security forces position this [Monday] morning at Amdjerima," said government spokesman Hourmadji Moussa Doumgor in a statement.
He said 38 rebel vehicles had been destroyed and "many" rebel fighters killed, along with eight Chadian soldiers.
Chad's information minister called on the international community to condemn Sudan for what he called its expansionist plans to destabilise his country.
However, another report quotes a Chadian official as saying they did pursue the rebels back into Sudan and then clashed with the Sudanese military.
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.
Relations between the neighbours have been strained for months despite a series of peace deals.
The UN 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.
Aid workers saw 'apocalyptic' destruction in eastern Chad
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 stabilise the eastern border region, although Chad says it only wants a police operation, not a military one.
Our correspondent says the 7,000-strong AU peacekeeping force is overwhelmed by the complexity and scale of the conflict in Darfur.
1. Chad says Sudan government-backed militias are attacking villagers in Chad. Some 200,000 Darfur refugees are also in Chad
2. Sudan accuses Chad of backing the Darfur rebels
3. Chad says it will send troops to help CAR fight the rebels
4. CAR says Sudan backs rebels who have seized towns in CAR
Are you in the region? Where do you think this is heading? Is war between Chad and Sudan a real possibility? Who should be doing what to broker peace?
This topic will form part of a discussion on BBC World Service radio. If you would like to take part please leave your phone number. No comments will appear on this page.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.