He also said that in the five months to the end of May this year France had sent back to Italy 10,249 migrants who had crossed their common border.
"I fear a major tragedy if states start refusing to accept rescued migrants", director general William Lacy Swing said.
Tria was due to meet French Finance Minister Bruno Le Maire in Paris later on Wednesday.
"If an official apology doesn't arrive, prime minister Conte would be right not to go to France", Salvini told reporters after demanding that France take in more migrants.
Foreign Minister Enzo Moavero Milanesi summoned the ambassador to a morning meeting "following the statements made yesterday in Paris on the Aquarius affair", his ministry said in an emailed statement on Wednesday.
France sought to take a more conciliatory tone on Wednesday. The Aquarius, with some 600 people saved from the sea over the last few weeks, is sailing to Spain after the country agreed to welcome the ship.
A government source said Conte still did not see the right "conditions" for a Friday meeting with Macron.
But after Italy and Malta refused entry to the ship, two Italian boats escorted the migrants to Spain - co-operated by SOS Mediterranee and Medecins sans Frontieres (MSF), who offered them "safe harbour".
Salvini insisted Tuesday that the country's ports would no longer be open to foreign boats carrying migrants. "We assure the Italian government of our complete support", he said, adding that he hoped Italy's stance "can bring a change to Europe's migration policy".
Under the EU's asylum laws - now the subject of revision amid a major political dispute - migrants must apply for asylum in the country where they first enter Europe.
After meeting in Berlin, Austrian Chancellor Sebastian Kurz and German Interior Minister Horst Seehofer echoed Salvini.
The German chancellor, who is working to pull together a Europe-wide deal on redistributing asylum seekers and find a more lasting solution to illegal migration involving enhanced controls along the European Union's external border, has dismissed the plan as in breach of EU law. "Therefore I think that there must be many such kinds of cooperation, not just in this one direction". Italian maritime vessels, however, are still docking in its ports: on Wednesday, an Italian coast guard vessel docked in Catania, Sicily with 932 migrants aboard.
However, the Sea Watch is still waiting to pick them up after asking for a written guarantee that it will be allowed to dock in an Italian port.
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