"People are in distress, are running out of provisions and need help quickly", said Vincent Cochetel, special envoy for the central Mediterranean for the UN Refugee Agency. "But Italy has stopped bending its head and obeying".
Transport Minister Danilo Toninelli, who is nominally in charge of the ports, said: "Malta can not continue looking the other way when it comes to respecting worldwide conventions".
Malta on Sunday reiterated its refusal to accept the ship, ignoring calls from Rome.
The standoff is actually the third in recent weeks, after the outgoing government of Premier Paolo Gentiloni refused to let humanitarian aid groups dock in Italian ports until the ships' flag nations had formally requested permission.
Italy has had to deal with hundreds of thousands of migrants in recent years coming via Libya to reach Europe.
Earlier on Sunday, the charity SOS Mediterranee on Twitter that its rescue ship, The Aquarius, had taken on board 629 refugees and migrants, including 123 unaccompanied minors, 11 other children and seven pregnant women.
"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.
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SOS Mediterranee said Maltese search-and-rescue authorities were contacted by their Italian counterparts "to find the best solution for the well-being and safety" of the people on the ship.
However, the ship has been allowed to dock in the Sicilian capital, after Leoluca Orlando, the mayor of Palermo, defied the new Italian populist government's orders.
While she does call on the European Union not to leave Malta and Italy on their own, Metsola's dig at Muscat contrasts with the message of support relayed on Sunday by Opposition leader Adrian Delia for government's stand.
"We are concerned at Italy authorities' directions given to Aquarius on high seas. They manifestly go against worldwide rules and risk creating a risky situation for all those involved".
By law, it'll be hard for Italy to refuse a safe haven according to Reuters.
Maltese Prime Minister Joseph Muscat said Italy's refusal to allow the Aquarius ship to dock at an Italian port risked "creating a risky situation for all those involved".
Salvini doubled down on his position, warning another charity ship, the Sea Watch 3, which is patrolling off the Libyan coast, that it may not be allowed to dock in Italy.
The Sea Watch still did not have any migrants on board, spokesman Ruben Neugebauer said.
Last week, Mr Salvini said Rome should increase its deportations of migrants.