The Aquarius, which is carrying 629 migrants who were pulled out of the sea by rescuers over the weekend, was left stranded between Malta and the Italian island of Sicily after Italy's hardline interior minister and leader of the anti-immigration League party refused to allow it to dock.
Spain's new Socialist prime minister, Pedro Sanchez stepped in Monday, ordering authorities in Valencia to prepare for the ship's arrival.
Both the ship and its passengers were caught up in a political dispute that might not have happened weeks ago. It added that the Aquarius "is still waiting for definitive instructions regarding the port of safety".
It was unclear if the days of sailing west it would take to get to Spain were feasible, SOS Mediterranee Maritime Operations Manager Antoine Laurent said.
The 629 migrants on board the MV Aquarius, a ship run by the French NGO SOS Méditerranée, have been transferred onto four smaller Italian boats. It came just after a fatal day in the Mediterranean, with at least 112 people estimated drowned when a boat that departed from the Tunisian coast sank at sea, and nine people, including six children, died in the Aegean Sea between Turkey and Greece.
Conte said Sunday that Rome had sent two patrol ships with doctors on board "ready to intervene and ensure the health of anyone on board the Aquarius who might have the need".
"Disembarkation can not be delayed further", said Dr David Beversluis, MSF's doctor on board Aquarius.
"All the survivors are exhausted and dehydrated because they spent many hours adrift in these boats", he said.
But a spokesman for Macron's Republic on the Move party said the Italian government's policy was "sickening". Like the Aquarius, the Sea-Watch 3 rescued migrants in the waters off Libya, where human smugglers are based and asylum-hopefuls have reported torture, beatings, rape and scarce rations in migrant detention centers.
Anelise praised the teams of staff on the vessel: "The teams here are very calm, they say the situation is under control and we continue heading north towards the east part of Malta and towards Italy".
The Aquarius ship at sea. Since we've been on air, the process of moving the migrants on to the Italian vessels has been completed.
Spain's offer is "important news, since it signals a turning point", Di Maio said.
Earlier on Tuesday the French government defended its decision not to offer safe harbour to the stranded migrant ship Aquarius after local leaders on Corsica proposed opening one of their ports to the vessel.
Macron's spokesperson, Benjamin Grivaux said France doesn't want to "start a precedent" that would allow some European countries to breach worldwide laws and rely on other EU member states.
"While Italy and Malta must open their ports, other European Union countries must share the responsibility for offering protection, rescues and asylum-processing".
"The duty of a democratic government is not to look away" in a humanitarian crisis, said Barcelona Mayor Ada Colau, who also offered her port as a potential solution to the standoff.
Malta and the new populist government in Italy each refused to take the migrants in, accusing one another of failing to meet their obligations.
Maltese PM Joseph Muscat also posted a thank you message on Twitter that blamed Italy for the ship's prolonged journey. The better option would be to disembark the rescued people in the nearest port, after which they can be transferred to Spain or other safe countries for further care and legal processing.
Human rights groups oppose returning rescued migrants to Libya, where many are held in inhumane conditions, poorly fed and often forced to do slave labour.