Three migrants died in the Mediterranean on Monday night, a German aid group said, during Italian-led rescue operations in which thousands more were pulled to safety from rickety boats.

About 5,000 migrants were picked up off the Libyan coast by emergency services, Italy's navy, aid groups and private boats on Monday, and rescues were continuing on Tuesday, according to an Italian coast guard spokesman.

"Despite all efforts, three people died from a sinking rubber boat" and rescue boats in the area are struggling to cope, German humanitarian group Jugend Rettet said on Facebook.