President Dioncounda Traore set out his position after France called for peace talks between Mali's government and "legitimate representatives" from the north.
Traore said he was ready for talks with the secular Tuaregs of the National Movement for the Liberation of Azawad (MNLA).
But he would not meet any of the three Al Qaeda-linked groups that seized
northern Mali last year, including the homegrown group Ansar Dine, (Defenders
of the Faith).
"It is obvious that Ansar Dine is now disqualified, not eligible for dialogue, whatever clothes they come garbed in," Traore said.
On Wednesday, with French troops at Kidal, the last of the major northern towns still held by the Islamists, Paris called for the dialogue to start.
"Only a north-south dialogue will prepare the ground for the Malian state to return to the north of the country," foreign ministry spokesman Philippe Lalliot said.
Bamako should talk to "non-terrorist armed groups" that recognised the integrity of Mali, he said.
Kidal, 1,500 kilometres northeast of the capital Bamako, was until recently controlled by the Islamists of Ansar Dine. Now the newly formed Islamic Movement of Azawad (MIA) claims control of the city and on Wednesday a spokesman said its leader was speaking to the French forces there.
The MIA on Monday announced it had split from Ansar Dine, saying it rejected "extremism and terrorism" and wanted a peaceful solution to Mali's crisis.
On Wednesday, it appealed to the international community to prevent the deployment of Malian and West African troops in the Kidal region before a political solution had been found.
But Traore told RFI: "This MIA story doesn't hold water”.
"Because fear has now changed sides, they are looking for a way out," he said.
"The only group we would consider holding negotiations with definitely is the MNLA, provided the MNLA waives all territorial claims," he said.
It was the MNLA who launched offensive in the north of the country in January 2012 in pursuit of an independent homeland for the Tuareg people.