Italian Interior Minister Matteo Salvini told Wednesday's Corriere Della Sera newspaper that ships belonging to foreign organisations and flying foreign flags could not dictate Italy's immigration policy. He also said that in the five months to the end of May this year France had sent back to Italy 10,249 migrants who had crossed their common border.
A day after French President Emmanuel Macron said Rome had acted with "cynicism and irresponsibility" by closing its ports to a migrant ship, Italy's economy minister cancelled a Paris meeting with his counterpart, and Prime Minister Giuseppe Conte weighed postponing a meeting with Macron scheduled for Friday.
"Our history of solidarity, humanity and welcoming spirit does not deserve to be criticised by members of the French government".
Kurz, who leads a coalition government with the far-right, anti-immigration Freedom party, said a growing number of European governments were now agreed on the need to curb uncontrolled migration and crack down on people trafficking.
The episode, coming a week after the installation of Italy's new anti-establishment government, has heightened tensions within the European Union over migration.
"The Italian government has never abandoned the nearly 700 people aboard the Aquarius", it said in a statement on Tuesday.
France tried to take a more conciliatory tone on Wednesday. "After the refusal of Malta to allow the people aboard the Aquarius to disembark there, we received an unprecedented gesture of solidarity from Spain".
"I'm pleased that they [France] have discovered responsibility".
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".
German Chancellor Angela Merkel has drawn criticism from her own conservative party for her open-door migrant policy, adopted in 2015, which also provoked a rise in support for the far-right Alternative for Germany (AfD) party.
"I fear a major tragedy if states start refusing to accept rescued migrants", director general William Lacy Swing said.
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"Finally!" said Hungary's anti-immigration Prime Minister Viktor Orban said at a meeting with his Slovak counterpart Peter Pellegrini on Tuesday.
Under the EU's asylum laws - now the subject of revision amid a major political dispute - migrants must apply for asylum in the country where they first enter Europe.
More than 1.8 million migrants have entered Europe since 2014.
"It's very clear that Europe needs to reform its asylum system in a collective manner; there's a lot of resistance to that but there's no other way", Grandi said.