"It can go where it wants, not in Italy!" far-right Interior Minister Matteo Salvini said, while mentioning France, Germany, Britain or Malta as destinations for the ship.
Adding: "Stop human traffickers and their accomplices, #closedports and #openhearts".
The Aquarius, rented by the SOS Mediterranee NGO and managed in partnership with Doctors Without Borders (MSF), was at the centre of worldwide spat in June when Italy and Malta both refused to lot it dock.
Italy has refused entry to charity rescue boats since a populist government came to power in June with a vow to make its European neighbours take more migrants.
Official sources in Spain say they are reluctant to accept more migrants because worldwide law calls for the country nearest the rescue, in this case Italy or Malta, to be responsible for the refugees.
They boarded their boat, the Aquarius, and tried to dock in Italy.
The director of the French port of Sete on the Mediterranean coast said meanwhile yesterday that he would be prepared to let the boat, carrying migrants mostly from Somalia and Eritrea to dock if the government gave the all clear.
A European Commission spokesperson said all diplomatic channels were being employed to find a country willing to take the migrants, .
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The MV Aquarius had started heading north on Sunday towards Europe when Libyan coastguards called the vessel to pick up 10 migrants spotted on a small fiberglass boat.
The vessel is reportedly now still at sea between Malta and Italy after MFS claimed both nations said they would not open their ports to the ship and those on board. The ship, he said, had a foreign crew and was now in Maltese waters, flying a Gibraltar flag.
The humanitarian groups said the Aquarius is adrift between Italy and Malta, and awaiting instructions.
"What is of utmost importance is that the survivors are brought to a place of safety without delay, where their basic needs can be met and where they can be protected from abuse", said the group's search and rescue coordinator, Nick Romaniuk.
The migrants were rescued last week after their two wooden boats capsized. "Spain is not the safest port", sources close to Spain's prime minster were reported saying by El Pais.
An estimated 720 people died in June and July when charity ships were mainly absent, Amnesty International estimates.
Protracted feuds between EU states over how to handle immigrants have thrown the issue back onto the European agenda.
"Policies created to prevent people from reaching Europe at all costs are resulting in more suffering and forcing those who are already vulnerable to take even riskier journeys to safety".