
The service said another vessel had issued an alert at 8am local time after sighting the semi-sunken black boat 48km south of Cape Sacratif in the city of Motril.
Rescuers found five passengers on the boat, three of whom were dead.
The two survivors were evacuated by helicopter to hospital and were in serious condition, suffering from hypothermia.
The survivors told rescue personnel that there had been 12 people on board when the boat left Algeria six days ago, prompting a search operation for the seven people believed to be missing.
The date and place of their disappearance was unclear, the service said.
It added that an airplane from European border agency Frontex was aiding in search-and-rescue efforts, which were hampered by strong winds causing waves of up to 3m in height.
The number of migrants arriving in Spain by boat in the first two-and-a-half months of this year quadrupled to 15,148 from the same period a year ago, interior ministry data showed.
Rights group Walking Borders said 6,618 people lost their lives during risky sea voyages trying to reach Spain in 2023.