Speaking at a press conference after meeting with a representative of the African Union (AU) regional organisation, Deby accused the AU of ignoring what he alleges is Sudanese government backing for militias seeking to destabilise his country.
"We are waiting for the AU to condemn this latest Sudanese aggression but it is not coming and we deplore this attitude", said Deby. "Since the start of the crisis in Darfur we have drawn the attention of the international community to this menace, but it has not responded."
The UN estimates more than 200,000 people have been killed as a result of worsening violence between the Sudanese government and rebel movements, which allege the neglect and oppression of the inhabitants of Darfur, a province in the south west of Sudan bordering Chad.
Deby accuses the Sudanese government of sponsoring militias to spread violence from Darfur into Chad, an accusation repeatedly denied by government officials in Khartoum. On Friday Chad cut diplomatic ties with Sudan and closed its main border crossing point.
UN Secretary General Kofi Annan on Monday called on the AU to maintain pressure on Chad and Sudan not to allow violence to escalate after last week's attacks, warning that "if there is another escalation in Chad you risk destabilising the whole region, not just Chad but also the Central African Republic, a sort of domino effect".
The Peace and Security Council of the AU met on Friday to discuss the attacks in Chad, when it condemned the rebel incursions, but also called on the Chadian government to open a dialogue with the other political actors ahead of presidential elections scheduled for 3 May.
The AU has been mediating erratic talks between the Sudanese government and two main rebel groups in the Nigerian capital Abuja for nearly two years. A deadline for agreement has been set by the AU for 30 April, although analysts are sceptical it will be met.