Salvini said France had taken in only a fraction of the 9,816 migrants it had pledged to welcome under a 2015 European Union relocation plan to relieve frontline countries Italy and Greece of the burden of caring for newly arrived migrants.
Macron initially did not respond to questions on the issue, but later told reporters: "We must never give in to emotions, which some people manipulate".
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.
The case has reopened one of the main unresolved faultlines in European politics: how to share responsibility for migrants trying to enter the bloc from conflict zones and poor countries, mainly across Africa and the Middle East.
But the talks were delayed as both countries traded barbs over the fate of more than 600 migrants rescued off the Libyan coast on the weekend.
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.
More than 1.8 million people have entered Europe irregularly since 2014 and Italy is now sheltering some 170,000 asylum seekers. The border crossing point at Ventimiglia has been the scene of protests and desperation for years as France has refused to let in migrants, many of whom are seeking to reach family in France or Germany.
France's leader had said Rome acted with "cynicism and irresponsibility" by rejecting the ship.
Italy's new economy minister Giovanni Tria had been due to meet his French counterpart Bruno Le Maire in Paris Wednesday afternoon.
Spain finally ended the deadlock Monday by saying the ship could land at its port of Valencia, with its arrival expected later this week.
Pope Francis has called for a "change in mindset" on migration policies, saying worldwide cooperation was vital, as Italy and France engaged in a diplomatic spat over the issue. At the moment the conditions (for the meeting) don't exist.
The two leaders also agreed to deepen cooperation on migration and to discuss new proposals ahead of the European Council summit at the end of June.
He said countries "must move from considering others as threats to our comfort to valuing them as persons whose life experience and values can contribute greatly to the enrichment of our society".