A La Gomera local government spokeswoman said it was hoped the blaze, which started on Saturday and has destroyed 700 hectares (1,750 acres) of farmland and woods, could be brought under control later on Monday if strong winds continue to abate.
“The bad news is that the fire is not receding,” she said, referring to the threat to the park. “The good news is that it is not advancing.”
The fire forced about 500 people to evacuate their homes but has now moved away from inhabited land.
Local radio reported on Monday that a farmer had been arrested on suspicion of accidentally starting the blaze while clearing land.
The Garajonay park is mostly covered in laurel forest and its lush vegetation is of a kind that has largely disappeared from southern Europe, according to UNESCO. (Reporting by Feliciano Tisera; Editing by Catherine Evans)