Ecuador’s decision to allow US planes to use a San Cristobal airfield prompts environmental concerns.
Opposition congressman Carlos Viteri said the agreement with the US was "unacceptable" and should be prohibited if "it intends to cede an inch of Ecuadorian territory".
Under Article 5 of Ecuador's constitution, the country is "a territory of peace" and the "establishment of foreign military bases or foreign facilities for military purposes shall not be allowed".
Ecuador's former president Rafael Correa also reacted angrily, tweeting (in Spanish) that the island was "not an aircraft carrier" for the Americans.
The Galapagos Islands, 563 miles (906km) west of continental Ecuador, are a Unesco World Heritage site renowned worldwide for their unique array of plants and wildlife.