Chad accuses Sudan of sheltering and backing Chadian rebels who attacked the border town of Adre last month. It has declared a "state of belligerence" with Khartoum.
The dispute is adding to insecurity in the Darfur region, where local militias backed by Khartoum have been raiding villages, occasionally straying over the border into Chad.
In recent months, scores of soldiers have deserted the army in Chad, Africa's newest oil producer, to join rebel groups near the large, arid country's eastern border with Sudan.
Khartoum denies backing Chadian rebels but the dispute has cast a shadow over its preparations to host an African Union summit from 23-24 January which Chad says should be held elsewhere.
Muammar Gaddafi, Libya's leader, offered to mediate and Chad said Idriss Deby, its president, met Gaddafi in Tripoli at the weekend and laid down four conditions to end the dispute.
Hourmadji Moussa Doumgor, Chad government spokesman said, Deby demanded Sudan disarm Chadian army deserters and other armed groups in its territory, turn them over to the UN refugee agency UNHCR, halt Sudanese militia raids into Chad and pay compensation for more than 600 Chadians killed in raids.
Doumgor said: "If these four conditions are met, Chad sees no obstacle to resuming direct contact with Sudan to renew the ancient ties (based on) non-interference in each others' internal affairs."
The Janjawid have been blamed
for border village attacks
Lam Akol, Sudan's foreign minister, said that Khartoum's policy was already to disarm armed groups, telling Radio France International: "We don't have Chadian rebels in Sudan to disarm.
"Nobody can close the border. The border is too long for any group, whoever they are, to close. But if the Chadians wish to put in place joint patrols with Sudan, we are ready to consider those things. We could have joint patrols to make sure nobody crosses into Chad and nobody crosses into Sudan."
The UNHCR and other aid agencies are providing assistance to camps on both sides of the border where many of the estimated two million Darfuris forced from their villages by nearly three years of violence have taken refuge.
Chad blames Sudanese Janjawid militias for attacks on villages near the border, and Doumgor said Sudan should pay compensation for 614 Chadians he said had been killed in such raids, as well as for thousands of head of livestock stolen.
Deby's government said an attack last Thursday left nine Chadian villagers dead and warned Khartoum that it would not let such attacks go unanswered much longer.
Chad has dispatched envoys around Africa to press its case against Khartoum, causing diplomatic ripples in advance of the African Union summit.
"We could have joint patrols to make sure nobody crosses into Chad and nobody crosses into Sudan"
Sudan's Foreign Minister
Host nations have traditionally assumed the continental body's rotating chair, but Chad has said it would oppose any move to name Sudan to the next chairmanship.
Sudan accuses Deby of using the dispute to deflect attention from his troubles at home after the army desertions and subsequent attacks on army bases in his capital N'Djamena.
Deby, who seized power in 1990 in a Sudanese-backed uprising, is fighting another diplomatic offensive after the World Bank froze aid and participation in an oil project due to Chad ending a scheme to save oil dollars for future generations.