Salvini, who is also deputy premier and the leader of the anti-immigrant Lega party, called on France to apologise and said he was not prepared to take criticism from a country which regularly stopped migrants on their shared border.
In a speech to the senate on Wednesday, Matteo Salvini - who is also Italy's interior minister and head of the nationalist League party - said that France had only taken in 640 of the more than 9,000 people it had promised to take from Italy.
Italy summoned the French ambassador for consultations Wednesday after France accused the new populist Italian government of cynical, irresponsible behaviour by refusing entry to a migrant ship, evidence that the standoff is having continent-wide repercussions.
Grandi applauded Spain for agreeing to take the ship but noted that Italy had borne the greatest burden of migrants arriving from Libya over the past few years.
Salvini, the leader of the far-right, anti-immigration League party, blocked the Aquarius from entering Italian ports this weekend, prompting an global outcry.
The vessel, carrying 629 migrants, is now heading to Valencia, Spain, escorted by two Italian ships.
"The same can not be said of France, which has often adopted much more rigid and cynical immigration policies".
Yet Slovakia's premier insisted that "we refuse to let migrants enter our country", a stance that could bring him into conflict with Italy's new leaders, who have called for the automatic, compulsory resettlement of migrants across all European Union countries.
Macron said Rome had acted "with cynicism and irresponibility" by turning away the migrant ship Aquarius.
Austrian Chancellor Sebastian Kurz hailed Wednesday an "axis of the willing" between the hardline interior ministers of Austria, Germany and Italy to combat illegal immigration into the EU. "We assure the Italian government of our complete support", he said, adding that he hoped Italy's stance "can bring a change to Europe's migration policy".
Mr Salvini said he plans to visit his conservative German counterpart in Berlin soon to hammer out new proposals on the boat row and the broader issue of migrant quotas.
The country has seen more than 700,000 migrants arrive on its shores since 2013.
The case touched on one of the main faultlines in European politics - how to share the responsibility of handling migrants trying to get into the bloc from war zones and poor countries, largely across Africa and the Middle East.
He demanded that France move from "words to action and offer a sign of generosity" by taking more in.
He has accused charities of working with human traffickers but said Italy would not stop rescuing migrant boats itself.
"We have put a stop to the NGOs".