Ban said before his two-hour meeting in the Chadian capital N'Djamena that he was encouraged that Deby had agreed to the deployment of a joint UN-European Union peacekeeping force on the eastern border and in the north of the Central African Republic.
UN police force Jean-Marie Guehenno, the head of UN peacekeeping operations, said the idea was for about 300 UN police to work with and train 850 Chadian police responsible for Sudanese refugee camps.
"Genocide is a crime against humanity as a whole, not just against it's immediate targets. It therefore falls on the world at large to act."
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Meanwhile, an EU force of some 3,000 troops would protect their zone of operations.
"The military is not focusing on the camps but the lines of communication are fragile. You have sort of roaming bands that can really make up a threat, first to the population and to any international deployment as they move around," he said.
France, the former colonial power in Chad and the Central African Republic, maintains a military presence in Chad and could provide half the men needed, Guehenno said.
But Thomas Merkelbach, the International Committee of the Red Cross representative in Chad, said the involvement of France "might become a problem" because the EU force "has to act and be perceived as being neutral".
France has lent Deby military support against the Chadian fighters active in the border region.
Deby said Chad was also offering to host a preliminary meeting for Darfur separatist leaders to smooth out obstacles prior to talks with the Sudanese government scheduled for October in Libya.
"Chad is one of the important regional players in addressing the situation in Darfur," Ban said.
Ban arrived in Chad from Khartoum where the Sudanese government agreed to take part in the peace negotiations.
Meanwhile, from N'Djamena, the UN World Food Programme appealed for emergency funds to feed the refugees and displaced civilians in the camps in eastern Chad.
The WFP said $81 million was required to feed the needy in 2008.
"Donors need to act now to avoid the risk of any delay in providing food for hundreds of thousands of people who entirely depend on WFP for their daily survival," Felix Bamezon, WFP country director, said in a statement.