There is no telephone appointment booking service. To make an appointment for a U.S. Citizen service at the Embassy or Consulate nearest you, please visit the State Department website:

U.S. Embassy in Quito: https://evisaforms.state.gov/acs/default.asp?postcode=QTO&appcode=1
U.S. Consulate in Guayaquil: https://cacms.state.gov/s/new-appointment

There is no walk-in service for U.S. citizens who require a service related to passports, citizenship, reports of birth abroad or notarial services. These services are by appointment only.