Italian Interior Minister Matteo Salvini told Wednesday's Corriere Della Sera newspaper that ships belonging to foreign organisations and flying foreign flags could not dictate Italy's immigration policy.
Salvini, who last week said he would not allow Italy to become Europe's "refugee camp", told the Senate he was open to a possible "axis" with Germany and Austria ahead of a key European Union summit at the end of June that will consider possible changes to asylum law to better share the burden of incoming migrants.
The Aquarius and two Italian ships that have taken some of the migrants are now expected to arrive in Valencia on Saturday night, weather conditions permitting, said SOS Mediterranee's co-founder Sophie Beau.
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.
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.
More than 1.8 million migrants have entered Europe since 2014, and Italy is now sheltering more than 170,000 asylum seekers, as well as an estimated 500,000 unregistered migrants.
Tria was due to meet French Finance Minister Bruno Le Maire in Paris later on Wednesday.
According to AFP news agency, citing a diplomatic source, the French ambassador will be received at 10:00 am (0800 GMT) at Farnesina, the seat of the Foreign Ministry in Rome.
Red Cross launching blood drive dubbed "Missing Types"
Blood use notification: Once a donation has been made, Whole Blood donors receive a notification when their blood has been used. The Red Cross wants people to recognize some misconceptions about blood donation as the organization looks for more donors.
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 relations between the two countries.
After meeting in Berlin, Austrian Chancellor Sebastian Kurz and German Interior Minister Horst Seehofer echoed Salvini.
France and Italy traded insults, rifts widened in Germany's ruling coalition and Austria called for an "axis of the willing" to take action as a simmering row over how Europe should handle irregular migration finally boiled over.
The vessel, run by charity organizations, was denied port entry also by Malta, and was eventually offered to dock in Spain.
"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.
On Wednesday, she said discussions between Italy, Germany and Austria were about finding "a Europe-wide solution. Therefore I think that there must be many such kinds of cooperation, not just in this one direction".
On Wednesday, an Italian coast guard vessel docked in Catania, Sicily with more than 900 migrants aboard in a sign that Italy under the populist 5-Star Movement and anti-migrant League is still accepting some migrants, but is forcing other countries to share the burden.
However, the Sea Watch is still waiting to pick them up, asking for a written guarantee that it will be allowed to dock in an Italian port.