Italy's new economy minister Giovanni Tria had been due to meet his French counterpart Bruno Le Maire in Paris Wednesday afternoon.
They were saved during several rescue operations off the coast of Libya.
Italian media said the fates of the two ships was evidence of the policy shift by Italy's new populist government: refuse entry to rescue ships of European-flagged aid groups, but allow Italian maritime vessels in its ports.
Lashing out at the French government, Salvini said France had taken in only a fraction of the 9,816 migrants it had pledged to accept under a 2015 European Union relocation plan. Italy for years has complained that it has been left largely alone to manage Europe's migrant crisis, but the new government says its tactics have finally gotten the point across.
The MEP also defended the approach of the sitting Italian minister of the interior, who denounced the "hypocrisy" of the French government, whose border with Italy is closed, in order to prevent migrants from crossing the Alps to reach France.
The Aquarius will now dock in Valencia, which is 800 miles from where the ship had been stranded.
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In a phone call with Italian Prime Minister Giuseppe Conte on Wednesday evening, "the president stressed that none of his comments were meant to offend Italy and the Italian people", Macron's office said in a statement.
The ship, escorted by two Italian vessels, is not expected to dock on the Italian island as it continues its journey to Valencia, Spain, where authorities have offered safe harbour for the 629 people the boat rescued from the Mediterranean last weekend.
France tried to take a more conciliatory tone on Wednesday. "We need to maintain dialogue", a source close to Macron said as the president visited the western town of Rochefort.
France claims it has received no formal request from Italy for an apology, believing the planned meeting between Macron and Conte would go ahead.
Macron's office said Tuesday that France doesn't want to "start a precedent" that would allow some European countries to breach global laws and rely on other EU member states to take in migrants.
The Elysee said in a statement Thursday that Macron and Conte spoke by phone on Wednesday amid an escalating clash between the two countries over migration.
"I am happy about the good cooperation that we want to develop between Rome, Vienna and Berlin - I think it marks very sensible cooperation that will contribute to reducing illegal migration to Europe", said Kurz, whose country assumes the EU's rotating presidency on July 1.