In an open letter posted on Facebook, Conte said he had convinced six European Union (EU) countries to take in the migrants aboard the Open Arms ship and accused Salvini of exploiting the immigration issue for electoral goals.
"It is time to insist towards a more European solution; otherwise Italy will find itself completely isolated in a situation which will become, once again, increasingly unmanageable," Conte wrote and added that he understands Salvini's "faithful and obsessive" treatment of immigration issues by reducing them to the "closed ports" policy.
However, "ultimately, if we really want to protect our ‘national interests,’ we cannot limit ourselves to exhibiting positions of absolute intransigence ... if we do not nourish the citizens' trust in public institutions, a short circuit will be created and eventually anger and disaffection will prevail. We must all work to give full dignity to the institutions we represent."
For his part, the far-right Minister Salvini replied by calling Conte's letter as a "humoral outburst" and ratifying his position regarding rescue ships.
"It is incomprehensible what Italy has to do with a foreign ship stranded in international waters? In what capacity are the Italian authorities expected to help,” the Interior Minister said.
"With me, the ports are and will remain CLOSED to the foreign traffickers and their accomplices. And it is clear that, without this firmness, the EU would never have moved a finger, leaving Italy and the Italians alone."
"The Facebook bickering between Conte and Salvini is beyond the sense of ridicule. A banana republic comedy. You failed, step down and go home without drama! Crisis of Government."
According to Conte's open letter, France, Germany, Romania, Portugal, Spain and Luxembourg "are willing" to redistribute some of the Open Arms' migrants into their territories.
This Spanish flagged boat has been in the Mediterranean for more than two weeks, waiting for some European country to offer a safe harbor to disembark 147 Africans.
Italian judges canceled on Wednesday the prohibition signed by Salvini against this rescue vessel. Nevertheless, the Open Arms remains off the coast of the Lampedusa port, for it has not yet received an authorization to dock.
In a similar situation is the Ocean Viking, a ship chartered by Doctors Without Borders and SOS Meditérranée, which expects a safe port with 356 migrants on board.
On August 8, Salvini, who is the leader of the League party, declared that the governing coalition is not viable anymore and announced the need to hold fresh elections.