A diplomatic standoff between Italy and France escalated on Wednesday as the two countries traded insults over migration policies.
"If an official apology doesn't arrive, Prime Minister Conte would be right not to go to France", Salvini told reporters.
In his speech, Salvini shot back and said France had turned back 10,249 migrants at Italy's northern border since January "including women, children and disabled people".
"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.
French President Emmanuel Macron said on Tuesday that Italy was "cynical and irresponsible" over the migrant vessel which had been left stranded in the Mediterranean after Italy and Malta refused to grant it permission to dock.
Italy has defended its decision to refuse to allow the Aquarius rescue ship to dock, saying it has never abandoned the ship and is escorting it to Spain.
Euronews correspondent Anelise Borges is on board the vessel, which is expected to arrive in Valencia in four days.
Macron's office said Tuesday that France doesn't want to "start a precedent" that would allow some European countries to breach global laws and rely on other EU member states to take in migrants. "Italy is right to say that this has to be shared more widely".
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.
France tried to take a more conciliatory tone on Wednesday.
The countries' two economy ministers also spoke by telephone, French finance ministry official said, and agreed to reschedule their cancelled meeting.
France is "perfectly aware" of the pressure on Italy as it copes with an influx of migrants from Africa, a foreign ministry spokeswoman said.
But Italy's foreign minister, Enzo Moavero, kept up the barrage by telling a French envoy that Macron's comments were "unjustifiable" and had compromised bilateral relations.
Salvini also told the Senate he was open to a possible "axis" with Germany and Austria on immigration ahead of a key European Union summit at the end of June that will, in part, consider changes to European Union asylum law to better share the burden of incoming migrants.
Amid mounting cross-party concern that German asylum policy is in disarray, Seehofer, of the Bavarian conservative CSU party, met Austria's chancellor, Sebastian Kurz.
"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. "Therefore I think that there must be many such kinds of cooperation, not just in this one direction".