Blocking ships from disembarking rescued passengers could discourage both nongovernmental organizations and merchant vessels from responding to boats in distress.
Austrian Chancellor Sebastian Kurz on Wednesday hailed cooperation between the hardline interior ministers of Austria, Germany and Italy on the issue.
"I'm glad the French have discovered responsibility".
"We believe an axis of the willing is needed to fight illegal migration", he said.
"We need to listen" to Italy, Grandi said, stating that the nation's populist government was "right to say" the nation can not welcome every boat of third world migrants wishing to make Europe their home.
"I fear a major tragedy if states start refusing to accept rescued migrants", director general William Lacy Swing said.
Salvini has repeatedly vowed to stem the flow of migrants to Italy, which has seen more than 700,000 arrive on its shores since 2013.
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.
Interior minister Matteo Salvini, who is deputy premier and leader of the anti-immigrant League Party, called on Mr Macron to apologise and said he was not prepared to take criticism from a country which regularly stopped migrants on their shared border.
Annelise Borges, a journalist for Euronews and NBC who was on board the Aquarius tells CNN that "everyone is extremely hot and very exhausted".
France was to have accepted a total of 19,714 migrants from Italy and Greece; in all, it accepted 4,677.
He demanded that France move from "words to action and offer a sign of generosity" by taking more in.
Italian maritime vessels that have picked up Europe-bound migrants in the Mediterranean still are entering the ports; on Wednesday, an Italian coast guard vessel docked in Catania, Sicily with 932 migrants on board.
The refusal to allow the ship to dock has been branded "shameful" by the United Nations refugee agency's chief Filippo Grandi, an Italian national.
Italy and Malta's rejection of the ship's passengers at the borders of their territorial waters, knowing some of those on board likely need worldwide protection, denied those passengers the opportunity to exercise their right under European Union, refugee, and human rights law to seek asylum.
Grandi, an Italian national himself, pointed out that Italy had taken the brunt of the massive numbers of migrants crossing the Mediterranean from Libya towards Europe in recent years.