Earlier this week, French Prime Minister Edouard Philippe expressed France's readiness to help Spain which accepted to receive the stranded migrants following Italy and Malta position.
Spain welcoming the ship was unexpected, but like Italy, the country just swore in a new government.
Amid rough seas, the Italian coastguard redirected the Aquarius rescue ship on Thursday along the east coast of Sardinia.
The migrants aboard the Aquarius, run by French NGO SOS Mediterranee, were stuck on the overloaded ship as Italy and Malta bickered over who should take them. The port is about 930 miles from where the vessel had been on standby since Saturday night.
"We hope this meeting will be able to take place very quickly", he said in a ministry statement.
But Italy's foreign minister, Enzo Moavero, kept up the barrage by telling a French envoy that Macron's comments were "unjustifiable" and had compromised bilateral relations.More news: South Korea mulling tour programmes in North Korea
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French President Emmanuel Macron harshly criticized the decision, angering the Italian side.
Italy's new Economy Minister Giovanni Tria meanwhile announced he was cancelling a meeting with his French counterpart Bruno le Maire in Paris.
France, she added, had also taken the second-biggest share of migrants relocated from Greece and Italy. "I want to work serenely with all, but with one principle: #Italiansfirst", Mr Salvini said on Twitter.
"I think we've never been so central and so heard as we have been over the last hours", Salvini told senators, adding that he had heard from sympathetic officials in Germany and elsewhere applauding his stance. "We need to maintain dialogue", a source close to Macron said as the president visited the western town of Rochefort.
Salvini has accused European aid groups of essentially operating taxi services for Libya-based human traffickers and said Italy will now refuse their rescue ships entry. As Italy has previously allowed government vessels to disembark migrants without incident, Sea-Watch expressed hope that the Trenton would be permitted to bring the survivors to shore herself if Sea-Watch 3 is blacklisted.
French charity SOS Mediterranée said Thursday that the Italian coast guard vessel guiding the Aquarius ship had chose to divert the convoy north along the east coast of Sardinia to bypass four-metre high waves and winds of 35 knots (65 km/h).
The U.S. Sixth Fleet said it was coordinating with its partners on where the migrants will go next.