"France says that we are cynical but between January 1 and May 31 it turned back 10,249 people at the border, including women and disabled children, " Salvini stated.
France was to have accepted a total of 19,714 migrants from Italy and Greece; in all, it accepted 4,677.
Macron and new Italian Premier Giuseppe Conte were scheduled to meet in Paris on Friday, but the Italian news agency ANSA said Wednesday that the meeting might be postponed because the conditions weren't right.
Earlier this week, French Prime Minister Edouard Philippe expressed France's readiness to help Spain which accepted to receive the stranded migrants following Italy and Malta position.
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.
"The detour of the Aquarius is clearly a symbol of the failure of the European Union and European governments with their contradictory policies", the head of MSF Spain, David Noguera, told AFP by telephone from Barcelona.
The refusal of Italy and Malta to take in the rescue ship Aquarius packed with migrants this week has shone a light on the flaws of European solidarity and underlined the urgent need to reform the Dublin asylum system.
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Aquarius had conducted the rescue operation off the coast of Libya on June 9. SOS Mediterranee said they had received food aid and supplies from the Maltese Navy and Italian Coast Guard.
The ship was eventually rerouted to Spain, after Spanish authorities said it would be allowed to dock in Valencia.
The migrants had boarded that truck near the village of Morahalom, at Hungary's southern border with Serbia, before heading toward Austria.
"Italy can not accept hypocritical lessons about migration from countries that have always preferred to look away", said a statement from the office of premier Giuseppe Conte.
This is the first time Italy has turned away a vessel since the start of the Mediterranean migrant crisis in 2013, and signals the determination of the new interior minister Matteo Salvini to "fulfil his campaign pledge" to stem the flow of migrants from Libya, says Nicholas Farrell in The Spectator.
He has accused charities of working with human traffickers but said Italy would not stop rescuing migrant boats itself.