A group of 69 migrants on a rickety wooden boat were rescued Sunday off Malta, the navy said, while 49 more were still at sea waiting for a country to allow them to dock.
The migrants sent out a distress call 117 nautical miles southwest of Malta and a Maltese navy vessel was sent to their aid, a statement said.
Meanwhile, the German NGO Sea-Eye said its rescue ship was responding to a report of another boat in difficulty with 24 migrants on board.
The German-flagged ship already has 17 migrants from West Africa on board who were rescued on Saturday in international waters off the coast of Libya.
At the same time, the Dutch-flagged Sea-Watch said it already had 32 migrants rescued on December 22 including three young children, three unaccompanied adolescents and four women from Nigeria, Libya and Ivory Coast.
While Italy, Malta, Spain and the Netherlands have refused to accept the Sea-Watch 3 migrants, several German cities have offered to take them in.
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On Saturday a government spokesman, however, said Germany would only accept some of the migrants if other European countries also agreed to do so.
Last week, a newborn baby and his mother were helicoptered from a boat to Malta.
More than 1,300 migrants have perished trying to reach Italy or Malta since the beginning of the year, according to the International Organization for Migration (IOM).