The fire, which has been burning for two weeks on Isabela, the largest island in the chain, was stopped less than two miles south of the Sierra Negra volcano, home to some 6,000 tortoises.
A spokesman for the Charles Darwin Institute on nearby Santa Cruz island said on Sunday that firefighters managed to hold back the fire by digging trenches on two fronts.
Two-thirds of the length of the fire had been controlled. Authorities were considering using tractors to move the tortoises, which can weigh up to 550lb each.
Winds that had fanned the blaze died down on Sunday, slowing the advance of the fire, which had reached a damper area of vegetation after burning its way through 16,000 acres of dry brush.
The fire was apparently started on 11 April by poachers on the sparsely populated island, which is 80 miles long and 30 miles wide.
The Galapagos, 600 miles west of Ecuador, are home to endangered species such as the marine iguana and flightless cormorant.