Despite efforts by both sides to play down their testy exchanges, the clash underscores the deep divides in Europe on how to deal with another summer surge in migrant arrivals from across the Mediterranean.
"It's time for collective action," Macron said Thursday during a trip to Rochefort, France.
"Sometimes finding solutions involves legitimate tensions when people disagree, but they disappear when people are willing to work together."
Yet there are few signs that European leaders are anywhere near being ready to formulate a common response to the hundreds of people arriving daily -- mainly on the coasts of Italy and Greece.
The issue of how to share the migrant burden is expected to dominate an EU summit at the end of June, which is supposed to be the deadline for an overhaul of the bloc's "Dublin rules".
The rules say migrants hoping to apply for asylum must do so in the first country they enter, a policy which has placed a huge burden on Italy in particular.
The influx has encouraged the rise of far-right and populist parties -- leading most recently to Conte's nomination as prime minister in Italy's new anti-establishment and far-right government.
This week Conte's interior minister was a founding member alongside his German and Austrian counterparts of an "axis of the willing" to combat illegal immigration.
Their announcement was seen by many analysts as an implicit snub of German Chancellor Angela Merkel's efforts to find an EU-wide response.
Other countries meanwhile, such as Hungary, Poland, the Czech Republic and Slovakia, have either refused outright or resisted taking in refugees under a contested EU quota system.
The spat between Macron and Conte this week erupted after Italy refused to allow the Aquarius, a rescue boat carrying 629 migrants picked up off the coast of Libya, to dock on its shores.
The majority of the migrants are from Africa, while several others come from Afghanistan, Pakistan and Bangladesh, according to Medecins sans Frontieres Spain.
Macron blasted Italy on Tuesday for "irresponsibility" -- a claim quickly denounced by Rome, which refused to take accept any "hypocritical lessons".
Many critics agreed that Macron was hardly in a position to lecture, saying France has accepted far fewer migrants than other EU countries, and its border police routinely send back migrants trying to cross into the country from Italy.
His comments prompted Rome to summon the French ambassador and cancel a meeting between the two countries' economy ministers this week, and cast doubt on whether Conte's lunch in Paris would still take place.
Macron's office said Thursday that the two leaders had spoken by telephone, and that "none of his comments were intended to offend Italy and the Italian people".
It also said Macron had called for closer cooperation between Rome and Paris to try to check the migrant flows at their source -- currently mainly in Africa.
Later the French foreign ministry said it was ready to welcome migrants aboard Aquarius who "meet the criteria for asylum" after they arrive in Spain.
Italy itself appeared eager to avoid too harsh a response, with a coast guard ship carrying over 900 migrants landing on Sicily on Wednesday.