Macron had on Tuesday 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 France's ambassador over Macron's comments and suggested a planned meeting between Macron and Italian President Giuseppe Conte in Paris on Friday could be cancelled unless Paris issued an "official apology".
As the war of words intensified, Italy's new economy minister shelved a meeting Wednesday with his French counterpart in Paris.
But the tensions appeared to have ebbed after a telephone call 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.