The event was postponed on Wednesday after al-Bashir failed to show up, telling mediators he had a headache due to travel.
Mediators hope the peace pact will end years of hostility between the two countries that has brought them close to war and spurred the conflict in Sudan's Darfur region.
But fighters from both Chad and the Darfur region - seen by many as fighting a proxy war for al-Bashir and Deby respectively - dismissed the planned pact.
They criticised it for failing to include them and said it would not bring lasting peace.
'Going nowhere'
"It's going nowhere. It's just a protocol, a ceremony," said Ali Ordjo Hemchi, a representative of the Chadian National Alliance, whose forces raided the country's capital N'Djamena last month.
"They can sign, but it's not going to produce anything."
Hemchi noted that at least five previous accords, brokered mostly by Libya but also by Saudi Arabia, had collapsed.
Armed groups in Sudan took a similar line.
Abdel Wahed Mohamed Ahmed al-Nur, chairman of the Sudan Liberation Army, said: "The Khartoum government has signed agreements with Chad ... agreements with the United Nations. And still our people are getting killed."
Kept waiting
The lack of trust between the two leaders was evident when Ban Ki-moon, the UN secretary-general, waited at the Senegalese presidential palace on Wednesday to meet al-Bashir.
He and Deby left the palace just before midnight without having met al-Bashir.
Abdoulaye Wade, Senegal's president, said: "I had a telephone call from President Bashir who told me: 'President Wade, I very much regret it, but I have travelled a lot and I have a headache. I cannot come in this state but I ask you to postpone the meeting until tomorrow morning."
The border area between Sudan and Chad has become a battleground for armed groups fighting both in Darfur and in eastern Chad.
Recriminations
Khartoum and N'Djamena accuse each other of supporting one or more of these groups.
Al-Bashir, who accuses Deby of failing to respect previous deals to stop backing anti-Khartoum fighters, has questioned the usefulness of another accord on paper.
About 200,000 people have been killed since 2003 in the Darfur conflict.
It pits the Khartoum government's forces and allied militia against local fighters who say the western region has been neglected and marginalised.