MUJAO said its branches "in several countries are ready to strike the interests of countries that intend to participate in the force of ECOWAS", warned spokesman Adnan Abu Walid Sahraoui in a written message to an AFP correspondent in the capital Bamako.
Mali has been gripped by chaos since disgruntled troops swarmed Bamako on March 22 and ousted the elected president of what had been seen as one of Africa's model democracies.
In the ensuing weeks, Tuareg rebels and Islamist hardliners have taken over a stretch of northern Mali the size of Afghanistan. Extremists have since imposed an austere version of sharia law in northern Mali.
The Islamists, also including Ansar Dine and Al-Qaeda in the Islamic Maghreb, and the Tuareg have since fallen out.
Witnesses told AFP earlier that Tuareg rebels left the historic city of Timbuktu on the orders of the armed group Ansar Dine.
Leaders of the Economic Community of West African States, or ECOWAS, were meeting in Ivory Coast meanwhile in a bid to end the crisis. The grouping is considering sending a military force to Mali.
