Goita met high-level civil servants in Mali's capital Bamako before declaring himself as the leader of the 'National Committee for the Salvation of the People'.
The group seized power on Tuesday in a coup that followed months of protests in the country, arresting incumbent President Ibrahim Boubakar and Prime Minister Boubou Cisse.
The African Union, European Union, the United States and the UN Security Council have all demanded their release.
The 'true force' behind the coup
"Mali is in a situation of socio-political crisis. There is no more room for mistakes," Goita, surrounded by armed military men, told journalists.
Reports claim that Goita, who is in his forties, was the head of Mali's special forces based in the centre of the west African country.
Several military men told AFP on condition of anonymity that Goita was the true force behind the coup.
Fellow coup chiefs meanwhile called on the public to return to normal life and warned against acts of 'vandalism'. They threatened to punish any soldier found guilty of extortion.
'Patiotic rally' on Friday
The opposition coalition M5-RFP promised to work with the junta to 'develop a roadmap'.
The coalition's Choguel Maiga told journalists they would 'organise the biggest patriotic rally on Friday' in Bamako and nationwide to 'celebrate the Malian people's victory'.
Macron calls for return to civilian rule
With Mali the cornerstone of French-led efforts to roll back jihadists in the Sahel, President Emmanuel Macron reiterated Wednesday his call to return to civilian rule.
"The fight against terrorist groups and the defence of democracy and the rule of law are inseparable," he tweeted.
La France et l’Union européenne sont aux côtés de la CEDEAO et de l’Union africaine pour trouver une issue à la crise malienne. La paix, la stabilité et la démocratie sont notre priorité.
— Emmanuel Macron (@EmmanuelMacron) August 19, 2020
Macron added that for French forces "to leave is to provoke instability and to weaken our fight. It is not acceptable."
According to analysts, the failure to roll back the jihadists was a major factor in fuelling frustrations with ousted Keita's rule.
