Aena said they had later downgraded the alarm from general to local, meaning the alert would not affect other flights.
Saudi Arabian Airlines flight SVA 226 was grounded before taking off after the pilot became aware of a note with a bomb threat, the Interior Minister Jose Fernandez Diaz said in parliament.
El Pais newspaper said the note, with "bomb threat" written in English, was pinned to a baggage compartment in the plane with a knife.
The plane, which was seen at the airport with the inflatable ramps extended and fire crew nearby, has since been isolated while an investigation is carried out.
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