A doctor on the ship, Dr. David Beversluis, said there were no medical emergencies onboard but one passenger had to be revived after he was rescued.
As the rhetoric intensified, the Aquarius remained on standby in the Mediterranean Sea with its 629 passengers, including 123 unaccompanied minors and seven pregnant women.
More than 600,000 migrants have reached Italy by boat from Africa in the past five years.
Salvini has accused the charities of acting as a "taxi service" for the migrants.
Italian Premier Giuseppe Conte said on Facebook that he had called on his Maltese counterpart, Joseph Muscat, to "explicitly at least take on the human assistance of persons in difficulty aboard the Aquarius".
Salvini took this a chance to remind that other European countries have been defending their borders without much of a fuss.
Despite the diplomatic pressure, Italy and Malta held firm, with Italian Interior Minister Matteo Salvini clearly using the high seas drama as a pretext to force the hand of Italy's European neighbors.
Dozens of people had spent nearly a full day in the water by the time the Aquarius reached them, Laura Garel, communication officer with SOS Méditerranée France, told CNN on Monday. "We need to have an idea of what port to go to, something that up to now we haven't had", Aquarius crew member Alessandro Porro told news channel Sky TG24 on Sunday.
The MV Aquarius rescue ship is seen as migrants on are rescued by the SOS Mediterranee organisation during a search and rescue (SAR) operation in the Mediterranean Sea, off the Libyan Coast, September 14, 2017.More news: No breakfast, IHOB is the International House of Burgers
The U.N. refugee agency said Monday that there was "an urgent humanitarian imperative" to act, calling on governments to accept the distressed migrants now and resolve "broader issues" later.
Doctors Without Borders, which has staff aboard the Aquarius, said the rescued migrants were stable for now but that food and water on the ship would run out by Monday night.
But the Spanish ports may be too far away for the overburdened Aquarius.
Italy's new rightwing government has closed its ports to the migrants rescued by a German vessel in Libyan waters.
It also said it requested help from the coastguard in Malta to send boats to aid the rescue mission but Malta refused.
"Our sole objective is to bring the people we've rescued, in hard conditions yesterday, to a port of safety", the group said in a statement.
It suggested that the hundreds on board "are running out of provisions".
"If a minister without heart lets pregnant women, children, elderly, human beings die, the port of Naples is ready to welcome them".
Left-wing mayor Luigi De Magistris said he would welcome in the humanitarian boat and added: "Naples is ready, without funds, to save lives".
But with 3,116 deaths in 2017, the Mediterranean remained the deadliest migrant route in the world past year, according to the IOM.
To the east, Libya's coast guard intercepted 152 migrants, including women and children, from two boats stopped in the Mediterranean off the coast of the western Zuwara district Saturday. If they're going to refuse to accept refugees picked up at sea, what basis do they have to criticize Italy for balking at taking in hundreds more of them every day?