This week, Italian and Maltese officials denied entry for the Aquarius, a ship carrying more than 600 Libyan migrants.
The issue arose when Italy's new populist government insisted that Malta take in the migrants rescued by the humanitarian ship Aquarius, which it refused to do.
In a phone call with Italian Prime Minister Giuseppe Conte on Wednesday evening, "the president stressed that none of his comments were meant to offend Italy and the Italian people", Macron's office said in a statement.
The ship was eventually rerouted to Spain, after Spanish authorities said it would be allowed to dock in Valencia.
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 bilateral relations. "Italy is right to say that this has to be shared more widely". Matteo Salvini accused France of turning back 10,000 migrants on its border with Italy.
SOS Mediterranee, the aid group that operates the Aquarius, said Thursday the Italian coast guard boat leading the convoy made a decision to skirt Sardinia's east coast after high waves caused exhausted migrants aboard to be seasick.
This undated photo released by by French NGO "SOS Mediterranee" on Monday June 11, 2018 and posted on it's Twitter account, shows migrants about to board the SOS Mediterranee's Aquarius ship and MSF (Doctors Without Borders) NGOs, in the Mediterranean Sea. Foreign Ministry spokeswoman Agnes von der Muhll said France was "fully aware of the burden that the migration pressure is placing on Italy" and that it was committed to cooperating with Rome on immigration.
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Grandi said that, even if the European Union succeeded in helping transit countries to manage the migrant flows before they arrive in Europe, "some people will continue to want to seek asylum in Europe".
"We believe an axis of the willing is needed to fight illegal migration", he said.
Mr Salvini also demanded that France "offer a sign of generosity" by taking in more migrants.
It added that Italy was waiting for French to take action to "heal the situation that has been created".
The French president's office said France didn't want to "start a precedent" that would allow some European countries to breach worldwide laws and rely on other EU member states to take in migrants. It coincided with growing tensions in Europe over Italy's refusal to let a migrant rescue ship dock, forcing other European countries to take them in.
Francis didn't refer to the dispute in his message, but echoed Italy's longstanding complaint that it has largely been left alone to cope with the hundreds of thousands of migrants who have landed on its shores in recent years.