"The island can not continue looking the other way when it comes to respecting global conventions", said the statement, which was signed by Salvini and Transport Minister Danilo Toninelli, who is nominally in charge of the ports.
SOS Mediterranee tweeted late on Sunday that the Aquarius had "received instructions from the Italian Maritime Rescue Coordination Centre to standby in our current position which is 35 nautical miles from #Italy and 27 nautical miles from #Malta".
Beau acknowledged that Italy, whose populist new government refused to allow the Aquarius to dock, must not have to "shoulder the burden alone" after taking the brunt of the migrant crisis for years as the main entry point from Africa.
Earlier in the day, the Maltese government also refused to accept migrants from the Acquarius.
"Italy broke worldwide rules and caused a stand-off", Maltese premier Joseph Muscat tweeted. "Malta will be sending fresh supplies to the vessel".
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".
In a statement, the Office of the Prime Minister said that the two leaders had discussed the current migration situation and that there was convergence in the two countries' policies.
Doctors Without Borders (MSF), which is operating the Aquarius alongside SOS Mediterranne, urged a rethink.
SOS Mediterranee director general Sophie Beau said Spain's offer "is encouraging and shows that some states are sensitive to the humanitarian emergency".
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European Union leaders in December had set an end-of-June deadline for an overhaul of rules to create a permanent mechanism to deal with migrants in the event of a new emergency.
However, Malta denied Italy's request and said that it has nothing to do with the rescue operation.
Italy claimed that Malta should accept the Aquarius because Malta was the safest, closest port to the ship.
"It's common sense. We ask that all of Europe assume responsibility for such a delicate and important issue as is immigration", he said in a TV interview.
Not everyone in Italy agreed with Salvini's hard line; the mayors of Naples, Palermo and Messina, said they would welcome the migrants.
"Naples is ready, without funds, to save lives", he said.
"You can't create a precedent that will enable one European country to offload onto other European countries", he continued.
The IOM and other humanitarian organizations argue it is not fair that a country such as Italy, which tends to be the first port of call, be responsible for the thousands of migrants that land on its shores. "They manifestly go against global rules, and risk creating a unsafe situation for all those involved", Mr Muscat said on Twitter.
"We call on all involved to contribute to a swift resolution so that the people on board the Aquarius vessel may be safely disembarked as soon as possible", Schinas said.