Dioncounda Traore, the former, speaker of the parliament, took the oath of office in the capital, Bamako, four days after President Amadou Toumani Toure handed in his letter of resignation to West African mediators.
The inauguration was attended by junta leader Capt. Amadou Sanogo, who led the March 22 coup but agreed under international pressure to hand back power to a civilian government.
In a speech, Traore, 70, called for talks with the separatist Tuareg rebels who capitalized on the post-coup disorder to capture large areas of Mali's vast Sahara region in the north.
But failing that, government forces will wage a "total and relentless war" to retake the captured territory, he warned.
The rebels have effectively split the West African nation in two, and northern areas remain volatile and tense, preventing aid agencies from accessing displaced people, the United Nations refugee agency said.
The rebels last week declared independence for a region they recognize as Azawad, the cradle of their nomadic civilization.
Calling for a return to peace, Traore urged all rebel movements "to return to the negotiating table and to the ranks to strengthen this nation instead of dividing it. I ask them to stop the atrocities, the looting, the rapes. I ask them to leave peacefully, now, the cities they have been occupying."
Traore said that his mission was to unify the country and that no split would be tolerated.
Foreign groups helping the rebels, such as al Qaeda in the Islamic Maghreb, the sub-Saharan offshoot of the terror group, would also be driven out, he said.
"We do not negotiate the split of the country," he said. "Mali will carry out this fight with the support of subregional countries, the whole of Africa, with the help and support of the European Union and the entire international community."
The March 22 coup staged by renegade soldiers led by Sanogo sparked a crisis in Mali, a West African nation that had been a cornerstone of stability.
The international community -- including West African states, the African Union and the United States -- called for the immediate restoration of constitutional rule.
Late last week, Sanogo reached a deal with the Economic Community of West African States, or ECOWAS, a regional group that promotes economic unity. The agreement mandated a handover of power to the civilian government in exchange for the end of trade and diplomatic sanctions.
The African Union and ECOWAS had slapped the military junta in Bamako with travel and economic restrictions, and froze its assets.
