A ferry alerted Spanish authorities that it had rescued 27 people from a small boat, the rescue agency said.
The Maritime Rescue Service said it confirmed with a non-governmental group that the boat left North Africa the previous day with 49 people on board. Surveillance aircraft and coast guard boats from Spain and Morocco were searching for it.
The ferry operator didn't find any other people at the scene.
Six migrants, including a young girl, were evacuated by helicopter for medical reasons.
Officials didn't immediately have further details. Spain is the biggest entry point for unauthorized migration to Europe from Africa.
Meanwhile, the German aid group Sea-Watch urged European governments to agree to accept several dozen migrants that it rescued in the Mediterranean a week ago.
Sea-Watch said Wednesday many of the 43 migrants still on board their boat were suffering from dehydration because of sea sickness, and other issues, the dpa news agency reported.
Over the weekend, Italian Prime Minister Matteo Salvini allowed ashore 10 of those rescued - those suffering from illnesses and families with children.
Germany's Interior Ministry says more than 50 German cities and towns have sent the federal government a written declaration that they are willing to take in migrants rescued from the Mediterranean. But it says the prerequisite for that would be "broad participation of the EU member states and coordination through the European Commission."
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