Two small boats from the MSF ship ferried across to the boat and handed out lifejackets before transferring the migrants aboard the Geo Barents.
The Alarm Phone hotline for boatpeople had earlier on Tuesday renewed its appeal for the authorities to stage a rescue.
Alarm Phone said it had managed to re-establish contact with the vessel, which is in the Maltese search-and-rescue area, after the first alert on Monday.
It said it had sent the updated coordinates of the boat's position to the authorities.
Alarm Phone said two merchant ships were near the boat but were "not equipped to complete such a big rescue operation".
Prime Minister Giorgia Meloni has called a meeting of top government officials on Tuesday to examine how to manage the big upswing in the number of migrants and refugees arriving in Italy via sea.
ANSA
