Touré said he had not been put under pressure to resign. In his first public appearance since going into hiding following the coup, he said "more than anything I do it out of the love I have for my country."
From Ouagadougou, Burkina Faso, President Blaise Compaoré, who played a key role in mediating the settlement, hailed the transition deal as a first step in restoring order to the troubled country.
Under the deal, speaker of parliament Dioncounda Traoré is to become interim president with the task of organising elections, if possible within 40 days.
But he also has to deal with the consequences of the uprising in the northern half of the country. Mali's northern half is now under the control of Islamist and Tuareg rebels.
Tuareg fighters there issued a declaration of independence Friday that was rejected not just by the international community but by their former allies, the Islamist militia.
According to the United Nations, more than 200,000 people have fled their homes in Mali since January, seeking refuge elsewhere in the nation or in neighbouring countries.
Amnesty International has warned of a major humanitarian disaster in the region.