In a statement, the AMN specified that the crew, three men aged between 50 and 60, of French nationality, are "physically well and have had no need to receive medical assistance".
According to the maritime authority, the alert was given at 9:30am, and the accident occurred after they hit a rock, resulting in water entering the vessel, which was partially submerged.
After the alert, the authorities deployed a semirigid boat from the Maritime Police and the Sagres Rescue Station vessel and an all-terrain vehicle was also activated.
The boat was about 500 to 600 metres east of Praia da Luz, in the municipality of Lagos, Faro district, in front of the place known as Rocha Negra.
"The National Maritime Authority is analysing the feasibility of its removal to a nearby port, since it represents a danger to navigation", the note reads.
According to the maritime authority, "the area surrounding the recreational boat has been analysed and there is no evidence of fuel, lubricants or pollutants spilling" at sea.