French President Emmanuel Macron criticized what he called Italy's cynicism and irresponsibility in turning away the Aquarius, which is operated by SOS Mediterranee and the French-founded Doctors Without Borders.
Italy's Foreign Ministry in Rome, where the French ambassador was summoned after a diplomatic spat over a stranded migrant ship.
He also said that between January and May, France had sent back to Italy 10,249 migrants who had crossed their common 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's new economy minister Giovanni Tria had been due to meet his French counterpart Bruno Le Maire in Paris Wednesday afternoon.
Visiting western France, Macron initially did not respond to questions on the issue, but later told reporters: "We must never give in to emotions, which some people manipulate".
The co-founder of the SOS Mediterranee charity says three ships carrying 629 migrants are expected to arrive around Saturday night at the Spanish port of Valencia, depending on weather conditions.
Many states have fallen short of their pledge, made in 2015, to take some asylum seekers from Italy and Greece - the first port of call for most migrants given their long Mediterranean coastlines - and share the cost of their care. The Aquarius was heading for Spain on Wednesday.
"Europe must stick together", she said, acknowledging Italy's concern that it had taken in many migrants but fellow European Union countries were not showing sufficient solidarity.
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.
Macron's office said Tuesday that France doesn't want to "start a precedent" that would allow some European countries to breach worldwide laws and rely on other EU member states to take in migrants. "We hope this meeting can take place very soon".
"I speak in the name of a government but I also have the ambition of speaking for a people who have nothing to learn from anyone about generosity, volunteerism, welcome and solidarity", he said.
As EU politicians have dithered or traded blame, refugees have continued to arrive.
An Italian coast guard vessel has docked in Sicily with more than 900 migrants aboard, evidence that Italy's new anti-migrant government is still taking in some asylum-seekers but is forcing the rest of Europe to accept others.
However, the Sea Watch is still waiting to pick them up, asking for a written guarantee that it will be allowed to dock in an Italian port.
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