"There is no positive change for the moment," an emergency official told reporters.
Firefighters on the ground were being helped by water-dropping aircraft, the report said.
The islands, located off the coast of Morocco, have experienced the driest conditions in some 70 years, the broadcaster said.
Adding to the woes, a heat wave from Africa last week created perfect conditions for the fires with temperatures above 100 degrees, low humidity and breezes.
The environmental secretary for the island of La Gomera, Ventura del Carmen Rodriguez, told reporters it would take at least 30 years for the nature reserve to recover from the fires.
Written by United Press International