Videos from the response on Saturday show helicopters scooping up large quantities of water before dropping it on affected areas.
The fire was covering an area of about six square kilometres.
Jon Henderson, SFRS assistant chief officer, said the response had been a “protracted effort” in difficult conditions.
However, he said firefighting work which began at about 04:30 on Saturday was beginning to yield some results.
He said: “The conditions have been very, very favourable, which has allowed us to really start to attack the fire in earnest and continue to contain it.
“The terrain is treacherous, it’s inaccessible at times, and it’s very, very difficult and very dangerous.
“We’re very positive about where we are now, but those things can’t change very quickly, and we need to remember that we’re dealing with a fire in a mountain range.”
