Diplomatic fight between Italy and France escalates.
But earlier, Italy's foreign ministry warned that relations had been compromised by France's public criticism that Italy's decision to refuse entry to the migrant ship Aquarius had been "cynical" and irresponsible.
"If an official apology doesn't arrive, Prime Minister Conte would be right not to go to France", Salvini told reporters.
"Our history of solidarity, humanity and welcoming spirit does not deserve to be criticized by members of the French government", he said.
The French foreign ministry responded that Paris was "perfectly aware of the weight of migratory pressure on Italy and the efforts of this country".
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. Italian maritime vessels, however, are still docking in its ports.
Some 629 migrants, mostly from sub-Saharan Africa, have been in the central Mediterranean since Sunday aboard the Aquarius, a vessel operated by SOS Méditerranée, a Franco-German charity that tries to rescue people making the risky crossing to Europe.
France sought to take a more conciliatory tone on Wednesday.
"So I ask President Macron to pass from words to action and tomorrow morning welcome the 9,000 France promised to welcome as a sign of concrete generosity and not just words", Salvini said to applause in the Senate chamber.
"I'm pleased that they [France] have discovered responsibility".
Macron said Rome had acted "with cynicism and irresponibility" by turning away the migrant ship Aquarius. "Let them open their ports and if they want we can send them a few people", he told reporters on Tuesday.
But there was also criticism from Spain, despite its gesture of solidarity.
This June 12, 2018 photo released Wednesday, June 13, 2018 by French NGO "SOS Mediterranee" shows migrants on the Aquarius ship after being rescued in the Mediterranean Sea.
"Finally!" said Hungary's anti-immigration Prime Minister Viktor Orban said at a meeting with his Slovak counterpart Peter Pellegrini on Tuesday.
But the talks were delayed as both countries traded barbs over the fate of more than 600 migrants rescued off the Libyan coast on the weekend.
"With my German and Austrian colleagues. we will propose a new (immigration) initiative", Salvini said, adding that it would apply both to the EU's external borders and to how the bloc's countries manage migrants internally.
Hours later, the Italian government said it could not "take hypocritical lessons from countries who have always preferred to look the other way on immigration issues".