Survivors rescued from the Mediterranean by the Aquarius, which is operated by the Medecins Sans Frontieres and SOS Mediterranee charities.
Spanish Prime Minister Pedro Sanchez, who took office just over a week ago, has given instructions for the boat to be admitted to the eastern port of Valencia, his office said in a statement.
Such rhetoric is largely symbolic as the MRCC in Rome is the only organization that can authorize the docking of a foreign-flagged ship in Italy - city mayors do not have the power to do so.
Italy's new interior minister, Matteo Salvini, said on Sunday that from now on, "Italy, too, begins to say NO to the trafficking of human beings".
"Malta is respecting worldwide rules and, therefore, can't let Aquarius dock at its port".
Malta, for its part, has consistently refused to take in migrants, citing its small size and limited capacities.
SOS Mediterranee spokesperson Mathilde Auvillain said the Aquarius had received orders to head north after a series of sea rescues and was now awaiting "definitive instructions".
Conte said that Italy has sent two patrol ships with doctors on board "ready to intervene and ensure the health of anyone on board the Aquarius who might have the need".
By law, it would be hard for Italy to refuse the boat a safe haven, as its own coastguard coordinated the rescues, picking up more than 280 migrants in its own vessels before transferring them to the Aquarius to be taken to safety. "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 in solitude". "We have never been a situation before where we have been denied a right to a port of safety", he said Monday via a WhatsApp message.
The migrants were rescued by Aquarius in six separate night-time operations in the central Mediterranean on Saturday.
"Particularly seven pregnant woman, 15 with serious chemical burns and several critical drowning hypothermia patients", MSF Sea said.
In defiance of Salvini, the mayor of Palermo, said he would allow the boat to dock in the Sicilian capital on Sunday night, however a journalist on board tweeted to say the boat had not moved since Sunday night.
Left-wing mayor Luigi De Magistris said he would welcome in the humanitarian boat and added: "Naples is ready, without funds, to save lives".
"Nevertheless I am very anxious for the direction taken by Italian authorities".
The same day Italian authorities held the migrant rescue boat Sea-Watch 3 for 12 hours after it brought 232 people to Reggio Calabria, on the south-western tip of the mainland.
This frame of a video taken by the Italian Coast Guard on January 6, 2018, in the Mediterranean Sea off Libya, shows migrants being rescued from dinghies as they try to cross to Italy.