The new leader faces the challenge of asserting control over northern parts of the country that are now controlled by Tuareg separatists, who have declared independence in the region they call Azawad, and other armed groups.
"I am president of a country that loves peace," Traore said after the swearing-in. "I call on the rebels to halt all abuses."
He said a peaceful route was the preferred option, but threatened all-out war if the separatists refused to agree to peace talks.
"We will not hesitate to wage a total and relentless war" unless the rebels left the cities they had occupied in the wake of the coup, Traore said, adding that he was prepared to negotiate with all groups apart from al-Qaeda.