The International Committee of the Red Cross, Unicef, and the UNHCR, said in a joint statement that most of the "orphaned" children actually appeared to have at least one parent.
After several days of talks with 21 girls and 81 boys aged between one and 10, the agencies said: "Ninety-one of the children referred to a family environment made up of at least one adult person whom they consider as a parent."
They also said the interviews "suggest that 85 of them come from villages in the border region between Chad and Sudan, in the area of Adre and Tine".
Adre and Tine are both in Chad.
The French foreign ministry has also joined the aid agencies in casting doubt on the claims by Zoe's Ark that the children were from Darfur.
But the nationalities of the children are still in question as thousands of people from Darfur have sought refuge in camps and villages in eastern Chad.
According to Annette Rehrl, a spokesman for the UNHCR, the children interviewed said "that they were living in Chadian villages for years, so they may turn out to be Chadian citizens, but until we go to their villages, we can't be sure".
Meanwhile, Idriss Deby, the president of Chad, said on state television that the journalists and flight crew among the 17 people who were arrested should be freed after a judicial process.
He said: "I hope that Chadian justice can very quickly shed light on this affair and that the journalists and the air hostesses, and those not involved, can be freed without delay."
Three of the nine French who are detained are journalists, and seven Spaniards are known to be part of the flight crew.
It was not clear if Deby was referring to the pilots of the plane who were meant to transfer the children to Europe.
A Belgian pilot is also being held.
Nicolas Sarkozy, the French president, called Deby on Thursday and according to David Martinon, the president's spokesman, the conversation "took place in an extremely positive atmosphere".
When asked about Deby's latest remarks, Martinon said: "We welcome this statement as an encouraging sign."
In a telephone conversation on Wednesday, Sarkozy urged Deby to free the French journalists.
The Republic of Congo has suspended all international adoptions following the events in Chad as "a preventive measure," Emmanuel Aime Yoka, the justice minister said.
Yoka said the Chad incident occurred only a few days after 17 children from the Republic of Congo were adopted by Spanish families.
He said the two events were not connected, but said the coincidence of timing led the government to re-examine its policies.
The government is taking measures to verify the situation of the children in Spain, he said.