Italy's new economy minister Giovanni Tria had been due to meet his French counterpart Bruno Le Maire in Paris on Wednesday afternoon.
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.
The asylum seekers remained stranded on the Aquarius vessel, run by French NGO SOS Mediterranee, while Italy and Malta bickered over who should accept them.
Spain finally ended the deadlock Monday by saying the ship could land at its port of Valencia, with its arrival expected later this week.
The incident prompted French President Emmanuel Macron to accuse Italy's new populist government of "cynicism and irresponsibility" for closing its ports to the 629 migrants.
Macron's comments sparked a fierce response from Rome, which called them "unacceptable" and summoned France's ambassador on Wednesday.
"Such statements are undermining relations between Italy and France," Italy's foreign ministry said in a statement on Wednesday.
Far-right Interior Minister Matteo Salvini further raised the stakes suggesting a planned meeting between the two countries should be cancelled if France did not issue an "official apology".
Prime Minister Giuseppe Conte and Macron are due to hold talks on Friday ahead of the European summit on at the end of the month, with a particular focus on migration.
"If an official apology doesn't arrive, Prime Minister Conte would be right not to go to France," Salvini told reporters.
Meanwhile, France said on Wednesday it regretted Tria's decision to cancel the meeting and remained "committed to cooperation and dialogue" with Rome.
France is "perfectly aware" of the pressure on Italy as it copes with an influx of migrants from Africa, a foreign ministry spokeswoman said.
"Axis of the willing"
Italy's rejection of the migrants has again highlighted the glaring differences between European Union member states over how to the issue of asylum seekers.
Austrian Chancellor Sebastian Kurz on Wednesday hailed an "axis of the willing" between the hardline interior ministers of Austria, Germany and Italy to combat illegal immigration into the EU.
"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.
"We believe an axis of the willing is needed to fight illegal migration."
EU leaders in December set an end-June deadline for an overhaul of rules to create a permanent mechanism to deal with migrants.
The International Organisation for Migration on Tuesday warned against the closing of borders in the bloc.
"I fear a major tragedy if states start refusing to accept rescued migrants," director general William Lacy Swing said.
"A sign of generosity"
Salvini has repeatedly accused fellow EU members of abandoning Italy as it struggles to cope with an influx of migrants making the perilous journey across the Mediterranean.
The country has seen more than 700,000 migrants arrive on its shores since 2013.
Under EU rules, migrants must apply for asylum in the European nation where they first arrive.
Speaking to the Senate on Wednesday, Salvini accused France of only welcoming 640 of the 9,816 migrants it had promised to take from Italy.
He also said that between January and May, France had sent back to Italy 10,249 migrants who had crossed their common border.
He demanded that France move from "words to action and offer a sign of generosity" by taking more in.
Salvini earlier underlined that Italy's ports would no longer be open to foreign boats carrying migrants.
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. The coastguard and navy can continue to save lives, but other countries need to keep giving us a hand," he said.
Meanwhile, an Italian coastguard ship carrying more than 900 migrants was allowed to dock in Sicily on Wednesday.