Macron had ignited the worst Franco-Italian diplomatic spat in years by accusing Rome of "cynicism and irresponsibility" for refusing to take in 629 migrants left stranded on a rescue ship that was eventually welcomed by Spain.
Rome summoned the French ambassador and cancelled a meeting between the countries' economy ministers, while threatening to call off talks betweenMacron and Italian premier Giuseppe Conte in Paris on Friday unless France issued an "official apology".
But the tensions appeared to have ebbed after a telephone call on Wednesday night between Macron and Conte.
"The president stressed that none of his comments were intended to offend Italy and the Italian people," Macron's office said in a statement. Friday's lunch meeting between the two leaders will go ahead as planned, the statement added.
Conte told reporters in Rome that the exchange was "very cordial". Asked whether he thought the row was over, he said: "I very much think so, yes."
"But now we need to work on reform of the Dublin Agreement," he added, in reference to controversial EU asylum rules.
The confirmation of his Paris visit came minutes after Italy's deputy prime minister Luigi Di Maio said Rome would "not back down" without a French apology. "The day when people thought they could make a mockery of Italy is over," Di Maio, leader of the Five Star Movement that shares power with the far-right League, was quoted by Agi news agency as saying.
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Photo: Kenny Karpov/SOS Mediterranee/AFP
The plight of the Aquarius rescue ship has shone a light on the failure of EU members to band together in the face of an unprecedented influx of migrants arriving across the Mediterranean since 2015.
Under EU rules, migrants must apply for asylum in the European country where they first arrive, putting pressure on Italy and Greece, the main entry points for people fleeing war and poverty in the Middle East, Africa and Asia. An EU scheme to distribute migrants equitably around the bloc has failed miserably, with central European members flatly refusing the quotas and others, including France, falling far short of their allocated target.
More than 700,000 migrants have landed in Italy since 2013. Many West Africans try to continue on to France, where they speak the language and often have relatives, only to find the border shut to them. Thousands of those who manage to sneak past controls through crossings in the Alps have been detained and sent back to Italy.
In a swipe at Macron, Italy's government said Tuesday it would not accept "hypocritical lessons from countries that have preferred to look the other way on immigration".
Photo: Giovanni Isolino/AFP
Macron told Conte he has "always defended the need for greater European solidarity with the Italian people" and called for closer cooperation between Rome and Paris to try to check the migrant flows at their source – currently mainly in Africa.
The issue of how to share the migrant burden is expected to dominate an EU summit at the end of June.
While Italy has taken much of the flak over the Aquarius, Macron has come in for criticism at home for remaining silent for two days while the ship was adrift, and then laying the blame solely at Italy's feet.
France's European Affairs minister Nathalie Loiseau on Thursday defended France's record.
"France last year received a record number of asylum seekers," she said, referring to the 100,000 asylum requests received by the country. France, she said, had also taken the second-biggest share of migrants relocated from Greece and Italy.
"We're doing a lot but it's true: Europe must do more and must do better to help Italy," she said.
By Clare Byrne