He said he had taken into account their demands over pay and conditions. There was no comment from the soldiers.
Writing on Twitter, Mr Ouattara asked troops to return to their barracks.
The mutiny began on Friday in the city of Bouake, and spread to the commercial capital Abidjan, where soldiers overtook the army headquarters.
They fired in the air as they took control of the base in the Abidjan’s Plateau district.
In his statement late on Sunday, the president said: “I confirm that I have agreed to take into account the demands of the soldiers over bonuses and better working conditions.”
Earlier on Saturday, firing was heard at the military base in Akouedo, on the eastern edge of Abidjan, which is home to parachute commandos that are considered loyal to Mr Ouattara.
Also on Saturday. Defence minister Alain-Richard Donwahi travelled to Bouake, Ivory Coast’s second city, to discuss the protesters’ demands. An MP in the city said the soldiers wanted $8,000 and a house each.
Similar protests were also reported in the cities of Man, Daloa, Daoukro, Odienne and Korhogo.
The BBC’s Alex Duval Smith in Ivory Coast says the mutiny has brought back memories of Ivory Coast’s 10-year civil war, which ended in 2011.
Some of the mutineers were thought to be former rebels who joined the army after the conflict.
The rebels swept into Abidjan from Bouake in 2011, helping Mr Ouattara take power after his predecessor Laurent Gbagbo – now on trial at the International Criminal Court – refused to accept defeat in elections the previous year.