About 600,000 litres (150,000 gallons) of diesel fuel have already escaped from an Ecuadorian tanker that ran aground off one of the islands last week. But American pollution experts joining the fight to contain the spill have warned that the Ecuadorian vessel is extremely unstable.
Ecuadorian Environment Minister Rodolfo Rendon said surf pounding the tanker Jessica had opened up new fissures in the ship's hull, speeding up the rate at which oil was leaking into the sea.
The US team is preparing to put a plastic barge next to the tanker and pump the remaining oil out.
Endangered species
"Our main concern is that the vessel is extremely unstable [and] virtually on the edge of capsizing," Commander Edwin Stanton of the US Coast Guard said.
Ecuador, which owns the islands, has appealed for more international help to contain the spillage, which has extended to an area of more than 1,200 square kilometres.
The Galapagos - where biologist Charles Darwin did much of his research - are home to rare species of birds and plants, and there are fears the spill may cause long-term harm.
Local people are trying to protect sensitive areas, such as beaches and sea lion colonies by physically lifting the oil out of the water. Conservationists are also trying to find a way of moving endangered species.
Birds covered in oil are being washed up on the shores, and advice is being taken from international bird research organisations. But there are fears that expected bad weather could worsen the situation.
'Deep impact'
Rodolfo Rendon said the islands' unique wildlife was seriously threatened by the oil spilt by the tanker, which ran aground 800 metres (2,600 feet) off San Cristobal island on Tuesday.
The vessel, which is owned by the company Acotramar, was transporting 900,000 litres (240,000 gallons) of oil. Officials say they have recovered at least 76,000 litres.
The international conservation group World Wide Fund for Nature (WWF) warned the spill could have "a deep and lasting impact" on local ecosystems, and called for limits to shipping in the area.
The clean-up operation has been complicated by the fact that chemical solvents usually used in oil accidents are not approved for use in the Galapagos' ecologically-sensitive waters.
Some animals are reported to have been evacuated from the island of San Cristobal. The oil threatens not only colonies of sea lions but groups of marine iguanas and birds such as blue-footed boobies.
The Galapagos Islands are Ecuador's main tourist attraction, famous for their giant tortoises. The animals on the islands provided material for some of Darwin's key research in formulating his theory of evolution.