"It is a horrible act which I say is a crime. I strongly condemn it," Deby said during a visit to a social centre in the town of Abeche, about 750km east of the capital N'djamena, where the children are being cared for.
"All administrative and judicial steps will be taken so that these people and their accomplices pay for their actions.
"The Chadian and Sudanese authorities must from now on put in place control systems so this never happens again," he said.
Arche de Zoe has said it moved the children out of Darfur, in western Sudan, to neighbouring Chad and was going to take them to France to "rescue them from death".
French authorities say they have started a judicial investigation into the group's activities.
Rama Yade, the French secretary of state for foreign affairs and human rights, condemned the charity's actions as "illegal and irresponsible".
She called the operation tantamount to "kidnapping".
Yade said: "We know absolutely nothing about how these children were gathered. We don't know their origins, their nationality or the reality of their family situation."
Marie-Roger Biloa, the founder and editor of Africa International magazine, told Al Jazeera that some organisations believe that they can go to Africa and grab children when they are in trouble.
Biloa said: "When the proper procedures are followed, and the parents agree to the children being taken away, can the process move forward. But in this case, some of the parents did not agree."
The UN Children's Fund (Unicef) said that the operation to try and bring the children out of Darfur "took place in violation of international rules."
Unicef, whose workers have been to the social centre in Abeche where the children are being kept, said they are mainly boys between aged between one and eight.
Jacques Hintzy, Unicef's French chief, said that most of the 103 children were not orphans.
According to Christophe Letien, a volunteer for Arche de Zoe, the arrests came after Chad's authorities changed their mind over the legality of the operation.
"We had formal statements from tribal chiefs and mayors that the children were indeed orphans, without mother or father," he said.
Yade, who travelled to Darfur this week, said the government had been aware of the planned operation for several months and had warned Arche de Zoe that it could be breaking the law.
The prospective families turned up at an airport east of Paris for the expected arrival of the flight from Chad.
Many spent the night at the airport and expressed fury at the detention of the charity's members.
"In no way we were seeking to adopt a child. We just wanted to offer a temporary family to a child who at a given moment in time had great need of one," said Andre Loudieres, 47, who drove nine hours from the southern town of Rodez.
Stephanie Lefebvre, secretary-general of Arche de Zoe, insisted the charity acted out of compassion and denied any plan to keep the children for adoption.
She said: "There has never - I repeat - never been any question of us being an adoption agency. These children were not intended for adoption."
"These children were abandoned, enlisted by warlords. Some were drugged and armed. In addition they were malnourished and in an alarming state of health."
She said a team from the charity had been in the region for two months, and that proper authorisation had been acquired from Chad officials.
A source close to Arche de Zoe said that the French military, which has a force in Chad, had helped fly its material into the east of country when it arrived in August.
Conflict in Chad has displaced an estimated 173,000 people in addition to 236,000 refugees from the Darfur conflict across the Sudanese border, according to UN figures.