Washington had described the reports as "very credible".
Deby on Friday said Abou Zeid, the Mali-based operative of al-Qaeda in the Islamic Maghreb (AQIM), was killed in fighting between Chadian troops and Islamist fighters on February 22.
"On February 22, we lost several soldiers in the Ifogha mountains after destroying the jihadists' base. This was the first time there was a direct confrontation with the jihadists," he said.
"Our soldiers killed two jihadist chiefs including Abou Zeid," said Deby, whose elite forces are among the best desert troops on the continent and have played a key role in the offensive to liberate northern Mali.
Algeria's independent Ennahar TV reported earlier this week that Abou Zeid was killed in northern Mali along with 40 other Islamist militants.
In Washington, a US official speaking on condition of anonymity said reports of his death seemed "very credible" and that if Abou Zeid was indeed slain "it would be a significant blow to al-Qaeda in the Islamic Maghreb".
French officials have so far reacted with caution, with President Francois Hollande saying Friday: "Reports are circulating, it is not up to me to confirm them."
The killing of Abou Zeid, a ruthless militant linked to kidnappings and executions of Westerners, would be a major success for French forces, who intervened in Mali in mid-January to help oust Islamist rebels then in control of the north.
The presidential election meant to haul Mali out of crisis will take place in July, the prime minister's chief of staff said Friday, without giving a precise date.
"Measures have been taken to respect the deadline," Boubacar Sow, chief of staff for Prime Minister Diango Cissoko, told AFP, a month after interim president Dioncounda Traore promised a vote by July 31.
"The security situation on the ground, a return to government in the north and of refugees and displaced residents are the prerequisites for which we are trying to find quick solutions," Sow said.
The elections are part of a roadmap adopted unanimously by parliament in January to restore constitutional rule in what was once considered one of west Africa's most stable democracies.
Critics have said July is too soon to organise the presidential and parliamentary polls given the problems Mali faces.
The French-led offensive continues to battle ongoing insurgent attacks in a nation weakened by a deeply divided military and where hundreds of thousands of people have fled their homes.
Algeria's El Khabar newspaper reported Friday that authorities there had carried out DNA tests to try to confirm Abou Zeid's death.
"The security services are comparing DNA taken from two close relatives of Abou Zeid with samples taken from the remains of a body supplied by French forces", it said.
French and west African troops have been hunting down rebels they dislodged from northern Mali's main cities following a lightning advance against the Islamists.
Abou Zeid, 46, whose real name is Mohamed Ghedir, was often seen in the cities of Timbuktu and Gao after the Islamists took control of northern Mali last year and sparked fears the region could become a haven for extremists.
An Algerian born near the border with Libya, Abou Zeid was a former smuggler who embraced radical Islam in the 1990s and became one of AQIM's key leaders.
He was suspected of being behind a series of brutal kidnappings in several countries, including of British national Edwin Dyer, who was abducted in Niger and killed in 2009, and of 78-year-old French aid worker Michel Germaneau, who was killed in 2010.
Abou Zeid was believed to be holding a number of Western hostages, including four French citizens kidnapped in Niger in 2010.
He was thought to have about 200 seasoned fighters under his command, mainly Algerians, Mauritanians and Malians, who were well-equipped and highly mobile.
An Algiers court last year sentenced Abou Zeid in absentia to life in prison for having formed an international armed group involved in the kidnapping of foreigners.
On the ground in Mali Friday, Malian troops arrested about 50 people near Gao on an island in the Niger river that was used as a hideout by armed Islamists, military sources told AFP.