In a phone call with Italian Prime Minister Giuseppe Conte on Wednesday evening, "the president stressed that none of his comments were intended to offend Italy and the Italian people," Macron's office said in a statement.
A lunch meeting between the two leaders in Paris on Friday, which Rome had threatened to cancel after Macron accused Italy of "cynicism and irresponsibility" in its response to the stranded Aquarius migrant ship, will go ahead as planned, the statement added.
The migrants were stranded on the NGO vessel Aquarius until Spain said the ship could land at its port of Valencia. It is expected to arrive there late on Saturday.
Macron accused Italy's new populist government of "cynicism and irresponsibility" for closing its ports to the 629 migrants, comments Rome blasted as “unacceptable”.
"Such statements are undermining relations between Italy and France," Italy's foreign ministry said in a statement on Wednesday after summoning the French ambassador.
Matteo Salvini, the powerful interior minister and deputy PM, said Conte’s meeting with Macron should be cancelled if France did not issue an "official apology".
His words were echoed by Luigi di Maio, another deputy PM, who said on Thursday morning that Rome was still waiting for an apology.
Italy's Economy Minister Giovanni Tria, meanwhile, announced he was shelving a meeting with his French counterpart in Paris, though French sources said the two ministers had agreed to meet “in the coming days”.
Macron has appealed for the two sides not to "give in to emotions that certain people are manipulating".
In a speech in the western French town of Mouchamps on Wednesday, he insisted that France was "working hand in hand with Italy" to handle migration.
From ‘words to action’
Italy has repeatedly accused fellow EU members of abandoning it as it struggles to cope with migrants making the perilous journey from Africa across the Mediterranean.
The country has seen more than 700,000 migrants arrive on its shores since 2013.
Speaking to the Senate on Wednesday, Salvini said France had received only 640 of the 9,816 migrants it promised to take from Italy under a 2015 EU deal that was never implemented.
He demanded that France move from "words to action and offer a sign of generosity" by taking more in.
Salvini, who heads the hard-right League party, has accused charities that rescue migrants of working with human traffickers but said Italy would not stop rescuing migrant boats itself.
An Italian coastguard ship carrying more than 900 migrants was allowed to dock in Sicily on Wednesday.
In Geneva, the head of the UN refugee agency (UNHCR), Filippo Grandi, also Italian, said Wednesday Italy was "right" to say it could not accept all the migrants crossing the Mediterranean.
"Closing ports, whoever does it, threatens rescue at sea, as we have seen in the case of the Aquarius, and therefore is not the right solution," Grandi told reporters in Geneva, though stressing that Rome’s reasons for closing its ports “have to be listened to”.
‘Axis of the willing’
European Union member states are deeply divided over how to deal with asylum seekers.
Italy and Greece, in particular, are angry at rules stating that migrants must apply for asylum in the European nation where they first arrive.
Antonio Tajani, the European Parliament's president, on Wednesday said the contentious issue was threatening "the survival" of the bloc, calling it "the biggest challenge of our times".
EU leaders in December set an end-June deadline for an overhaul of rules to create a permanent mechanism to deal with migrants.
German Chancellor Angela Merkel said the issue was "something of a litmus test for the future and the cohesion of Europe".
But as the 28-nation bloc struggles to reach a common stance, some countries have vowed to take matters into their own hands.
On Wednesday, Austrian Chancellor Sebastian Kurz hailed cooperation between the hardline interior ministers of Germany, Italy and his own country on the issue.
"I think it marks very sensible cooperation that will contribute to reducing illegal migration to Europe," said Kurz, whose country assumes the EU's rotating presidency on July 1.
"We believe an axis of the willing is needed to fight illegal migration," he added.