The 629 migrants, including pregnant women and scores of children, were saved by SOS Mediterranee on Saturday.
The Aquarius rescue vessel was however caught in a dramatic standoff over the weekend that saw Italy and Malta refuse to allow it to dock.
"Supplies will be received shortly from an Italian vessel onto #Aquarius. Plan from MRCC (the Maritime Rescue Coordination Centre) Rome is that rescued people will later be transferred on Italian ships before heading together to" the eastern Spanish port of Valencia, the charity said on Twitter.
The #Aquarius is now receiving supplies, coordinated by #Italian Rescue authorities. The intention of the Italian MRCC is to transfer some people from the #Aquarius to Italian ships & head to #Valencia, #Spain together. #MSF calls for people's safety to come before politics. pic.twitter.com/B6onGWvq19— MSF Sea (@MSF_Sea) June 12, 2018
The development comes a day after the new Spanish government headed by Socialist Prime Minister Pedro Sanchez offered to allow the Aquarius to dock in Valencia, insisting it was an "obligation" to do so.
The refusal to accept the Aquarius in Italy was the first major anti-migrant move since far-right Interior Minister Matteo Salvini took office this month.
Authorities on the French island of Corsica also offered to host the migrants, the morning after SOS Mediterranee raised fears that the Aquarius would not be able to reach Spain safely due to deteriorating weather conditions.
Aid workers had also warned that food and drink supplied by the Maltese navy to the migrants would only last until Tuesday.