The emergency services were alerted to the fire on a hillside at Loch Doon at 18:50 on Saturday.
At least five miles of hillside has been affected and the public have been asked to avoid the area.
East Ayrshire Council said overnight that progress had been made and that a welfare centre had been opened in the nearby town of Dalmellington.
The fire is burning on open hillside as well as the northern edge of Galloway Forest Park, on ground between Loch Bradan and Loch Doon.
Fire crews have been working in the area with support from Police Scotland and Forestry Commission Scotland.
They are expected to remain at the scene monitoring the site and managing hot spot areas till later this week.
The cause of the fire is still under investigation but the Scottish Fire and Rescue Service (SFRS) said recent dry weather has heightened the wildfire risk.
A Police Scotland spokesperson also advised the public to stay away from the area, saying: “Emergency Services continue to deal with a large wildfire in the area of Loch Doon, near Dalmellington. Members of the public are being asked to avoid the area as officers from SFR work to contain the fire.”
The blaze comes after SFRS chiefs warned on Friday, April 12, of increased risk of wildfire in the area.