Idriss Deby said Chadian forces killed Abdelhamid Abou Zeid during clashes in the remote region.
Abdelhamid Abou Zeid is said to be second-in-command of al-Qaeda in the Islamic Maghreb, which is fighting foreign forces in Mali.
The Algerian national is accused of killing two Western hostages – Briton Edwin Dyer in 2009 and Frenchman Michel Germaneau the following year.
His death will immediately raise questions over the state of several French hostages who are widely believed to have been in Abdelhamid Abou Zeid’s custody.
In January France sent some 3,500 troops to northern Mali to oust various Islamist militant groups who had seized a vast area of the Sahara desert.
Chad is one of several African countries to have supported the French operation.
After recapturing the region’s main towns, French and Chadian troops have been battling Islamist fighters in the Adrar des Ifoghas mountains north of Kidal, where the militants had regrouped, in recent weeks.
Algeria’s Ennahar TV reported earlier this week that Abdelhamid Abou Zeid was among 40 militants killed in the area near the Algerian border.
“Chadian forces killed two jihadi leaders, including Abou Zeid,” Idriss Deby said on Friday, without giving any further details.
President Idriss Deby was speaking after the funerals of Chadian soldiers killed in the fighting.
Algerian media have reported that security operatives have taken DNA samples from two of Abdelhamid Abou Zeid’s relatives to compare with the body which is reportedly his.
A US official – speaking on condition of anonymity – said Washington found reports that Abdelhamid Abou Zeid was killed “very credible”, according to the AFP news agency.
However, France reacted with caution to the reports, with government spokeswoman Najat Vallaud-Belkacem stressing that his death was so far unconfirmed.
Earlier unverified reports in the French media said that the militant was killed during fighting against French army units.
Abdelhamid Abou Zeid – believed to be in his 40s – was known as the most violent al-Qaeda commander in the region.
He was last seen in public in the Malian cities of Timbuktu and Gao seized by Islamist groups last year.
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