The ship is carrying 629 rescued migrants, who joined together in early morning prayers on board the Aquarius as Malta and Italy stood their ground.
Italy's spat with Malta began after its reported refusal to come to the aid of another rescue ship Seefuchs, which was stranded with 126 migrants on board due to violent seas until it was allowed to dock in the Sicilian port of Pozzallo on Saturday.
The Aquarius and its passengers were caught up in a crackdown promoted by the right-wing partner in Italy's new populist government, which has vowed to stop the country from becoming the "refugee camp of Europe".
"The people we saved yesterday were in a hard condition, at least 50 were at risk of drowning".
"We want to show that we were a very open port and now the European Union needs to take responsibility and it has to do it now".
Like Malta, Italy didn't appear to be budging.
The Aquarius carried out the rescue, with the help of Italian frigates, deep in Libyan search and rescue zone in the early hours of Sunday.
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"The Mediterranean is the sea of all the countries that face it, and it (Malta) can't imagine that Italy will continue to face this giant phenomenon (of migration) in solitude", the ministers said.
Italy's coast guard and navy and private cargo ships picked up 400 of the migrants before they were transferred to the vessel operated by humanitarian group SOS Mediterranee.
The Maltese Rescue Coordination Center "is neither the competent nor the coordinating authority", the statement said.
"Our only objective is the disembarkation in a port of safety of the people that we rescued yesterday in hard conditions", it said, adding that it "took good note" of the Italian Interior Ministry's statements.
"Our objective is the disembarkation in a port of safety of the 629 people now on board the Aquarius - some we rescued yesterday night in hard conditions", she was quoted by Reuters as saying.
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Among those on board are 400 migrants rescued by the Italian navy and merchant vessels before being transferred to the Aquarius. The rescuers say those on board the Acquarius include 123 unaccompanied minors, 11 children, and seven pregnant women.