He has repeatedly accused charities of working with human traffickers but said Italy would not stop rescuing migrant boats itself.
"The visit was canceled at Italy's request, and we regret it", the French source said, adding France had a lot of ground to cover with newly-appointed Tria.
Italy postponed high-level talks with France Wednesday after Paris blasted Rome for its "nauseating" refusal to take in a migrant rescue ship, in a major diplomatic spat.
Italy's new populist government came under fire Tuesday from its European Union neighbours after refusing to let a foreign NGO boat carrying 629 mostly African migrants dock in Italy.
Under EU rules, migrants must apply for asylum in the European country where they first arrive. Italy is now sheltering more than 170,000 asylum seekers, as well as an estimated 500,000 unregistered migrants.
Salvini's League scored its best result in the March national election, partly on pledges to deport hundreds of thousands of migrants and halt the flow of newcomers, and has formed a coalition with the anti-establishment 5-Star Movement.
The countries' two economy ministers also spoke by telephone, French finance ministry official said, and agreed to reschedule their cancelled meeting.
"Such statements are undermining relations between Italy and France", Italy's foreign ministry said in a statement Wednesday. Justice Minister Dolores Delgado said that Italy may have violated global humanitarian law, while Ximo Puig, president of the Valencia region, commented: "Turning this into a political weapon is despicable.it is clear that Europe must act more wisely, but we can not let these people die at sea".
After meeting in Berlin, Austrian Chancellor Sebastian Kurz and German Interior Minister Horst Seehofer echoed Salvini.
"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.
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".
As EU politicians have dithered or traded blame, refugees have continued to arrive.
Meanwhile, an Italian coastguard ship carrying more than 900 migrants was allowed to dock in Sicily on Wednesday.
A Dutch-flagged humanitarian ship, the Sea Watch 3, was called by a U.S. Navy vessel to take on board 41 survivors and 12 bodies recovered after a shipwreck on Tuesday.
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