"Such statements are undermining relations between Italy and France", Italy's foreign ministry said in a statement Wednesday.
Italy's Deputy Prime Minister Luigi Di Maio said on Thursday he still expects French President Emmanuel Macron to apologize for critical comments he made about Italian immigration policy two days ago.
The migrant ship Aquarius is now headed to Valencia in Spain.
United Nations refugee chief Filippo Grandi urged the European Union on Wednesday to sort out its "shameful" refugee policy after both Italy and Malta turned away a ship carrying hundreds of migrants.
"We have nothing to learn about generosity, voluntarism, welcoming, and solidarity from anyone", far-right Italian Interior Minister Matteo Salvini told the Senate.
"Spain wants to report us, France says I'm "nauseating".
A government source said Conte still did not see the right "conditions" for a Friday meeting with Macron. Mr Salvini said he plans to visit his conservative German counterpart in Berlin soon to hammer out new proposals on the boat row and the broader issue of migrant quotas.
Meanwhile, France said Wednesday it regretted Tria's decision to cancel the meeting and remained "committed to cooperation and dialogue" with Rome.
France said it has received no formal request from Italy for an apology, and that it believed the planned meeting between Macron and Conte would go ahead.
France tried to take a more conciliatory tone on Wednesday.
The line Italy drew with the Aquarius appeared to be a tactic by the populist government sworn in this month to force Europe's hand at a summit of European Union leaders in Brussels set for June 28-29.
He has accused charities of working with human traffickers but said Italy would not stop rescuing migrant boats itself.
Salvini also accused France of having turned back 10,249 migrants at Italy's northern border since January, "including women, children and disabled people".
More than 900 people have arrived at the Italian port of Catania in Sicily after being rescued at sea by the Italian Coast Guard. 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. German aid group Sea-Watch said the migrants were picked up after their rubber dinghy sank and the Navy also had recovered the bodies of 12 people.
Under the EU's asylum laws - now the subject of a major political dispute and under revision - migrants must apply for asylum in the country where they first enter Europe.