That left the migrants stranded until Spain offered to take them, although it.
The vast majority of the people travelling on the Aquarius - 400 - were rescued by Italian coast guard and navy vessels as well as cargo ships in the waters off Libya.
This would mean already exhausted people rescued have to endure four more days travel at sea.
Corsican leaders Gilles Simeoni and Jean-Guy Talamoni, the top politicians on the French Mediterranean island, tweeted their offer on Tuesday morning as uncertainty grew over the fate of the 629 people on board the ship.
The Aquarius, a rescue vessel operated by aid organizations Doctors Without Borders (also known as Médecins Sans Frontières) and SOS Mediterranée, was forced to wait in the Mediterranean Sea between Italy and Malta after failing to receive guidance from Italian authorities.
"It says that the country responsible for operations in that area has primary responsibility for taking them from the ship".
In a statement late Sunday after speaking with his Italian counterpart, Mr Muscat refused to let the ship dock in a Maltese port, but said Malta would conduct emergency medical evacuations if necessary. "629 immigrants overseas the ship Aquarius headed for Spain, primary goal achieved!" "All a political stunt ... at the expense of people in distress?"
But Italy can not simply expel hundreds of thousands of undocumented migrants without severe repression, and Italy doesn't yet have the agreements with many key countries of origin needed to facilitate returns.
The far-right League scored its best-ever result in March national elections and has formed a coalition government with the anti-system 5-Star Movement.
A little more than a week ago, Italy's new interior minister, Matteo Salvini, told a crowd that "Italy and Sicily can not be Europe's refugee camp" and "the good times for illegals are over", Deutsche Welle reports.
The ship was carrying 629 migrants rescued within the Libyan search and rescue region, making Lampedusa its nearest safe port.
Successive Italian governments have accused their European partners of leaving the country to cope on its own with an influx of 700,000 migrants from Africa since 2013. Migrant flows into Italy continue, albeit at a slower rate, and migrant departures from Italy to other European nations proceed at a relatively slow pace due to EU asylum policies. "We need to show solidarity which Italy has not shown".
Spain has offered to take them in, which Macron praised during the Cabinet meeting.
Gabriel Attal, a spokesman for Macron's party, told Public Senat TV: "The Italian position makes me vomit". In practical terms, no ships of this type will be able to land without cooperation of the Italian coastguard, which is under the direct command of the Italian government.
The mayor of Naples, who has repeatedly clashed with the League leader, said he would welcome the humanitarian boat.