"Food shortage, bad weather and a Spanish port too far away: faced with emergency, the Corsican Executive Council proposes to @SOSMedFrance to welcome the#Aquarius in a Corsican port," the body's Corsican nationalist president, Gilles Simeoni, tweeted on Monday evening.
Corsican executive council chief Gilles Simeoni offers to take migrants
Corsican Assembly chairman Jean-Guy Talamoni called on Europe to show solidarity on the question and said it was "natural" that Corsica accept the ship, whose passengers include 123 unaccompanied minors, 11 accompanied children and seven pregnant women.
It was unclear whether the pair could deliver on their offer, since the central government representative on the island, Josiane Chevalier, pointed out that such a decision would rest with Paris.
With 629 people on board, the Aquarius, which is equipped to take 500 passengers, could have difficulty with waves higher than two metres, the NGO that runs it, SOS Méditerranée, said on Monday.
But an offer by Spain's new Socialist-led government to take the migrants led to Italy providing two boats to help carry them to Valencia.
Macron slams Italy
French President Emmanuel Macron on Tuesday condemned Italy's "cynicism" and "irresponsibility".
He is to meet new Italian Prime Minister Giuseppe Conte at the Elysée Palace on Friday.
Foreign Affairs Minister Jean-Yves Le Drian called on Rome to change its mind because of the distance the boat has to travel to arrive in Spain.
The previous day Prime Minister Edouard Philippe, when challenged at a press conference with his Belgian counterpart, Charles Michel, simply called for Europe to adopt a "balanced policy" on immigration with an emphasis on working with countries of origin to "avoid departures".
The spokesman for Macron's Republic on the Move (REM) party Gabriel Attal was more forthright, slamming the Italian government's position as "sickening" and condemning "playing politics with human lives".
Right says no to accepting stranded migrants
Mainstream-right MP Eric Ciotti said there was no question that the Aquarius dock at Nice, the Riviera city in the area he represents.
"Certainly not, we don't want Nice to become Lampedusa," he told CNews TV, referring to the Italian island where many migrants land. "I hope the French authorities will be extremely firm, he went on, adding that "no French port, neither Corsica, nor Nice, nor Marseille" should take them in.
Spain's decision is "an error", Ciotti said. "The Italian government, by its firmness, will make things move ahead" and Europe should "ensure that the migrants no longer arrive in Europe".
Republicans spokeswoman Laurence Sailliet declared that "accepting this boat is accepting the work of the people smugglers", echoing far-right leader Marine Le Pen who tweeted that "beneath the humanitarian varnish" SOS Méditerranée play "the objective role of accomplices of the people smugglers' mafias".
Both Le Pen and Ciotti called for migrants to be sent back to where they have come from.
France stops border-crossings
About 700,000 migrants have landed in Italy since 2013 and France has prevented many of them crossing its borders.
A 2015 European Commission attempt to relocate about 100,000 asylum-seekers resulted in only 35 percent of the target being met on 31 May, with France only accepting 5,000, 25 percent of its target.
SOS Méditerranée said Tuesday the Aquarius would continue its operations.
An Italian coastguard boat, the Diciotto, was due to arrive in Sicily on Tuesday or Wednesday with 937 migrants on board.