Following the death of former president Giorgio Napolitano, aged 98 on Friday, Mr Macron was in the Italian capital to attend his state funeral.
Mr Macron and Ms Meloni had a “long and friendly meeting” after the ceremony, the Italian leader's office said in a statement.
Mr Macron and Ms Meloni, who last met in Paris in June, are both due at the “Med 9" summit of southern EU nations in Malta on Friday. There will also be an informal European Council meeting in Granada, in Spain, next week.
The French President's office confirmed the pair had discussed “the need to find a European solution to the migration question”, as well as economic issues.
A sharp rise in migrant landings on the Italian island of Lampedusa earlier this month reignited a bitter debate across the EU over who should take responsibility for asylum seekers.
There has been particularly heated rhetoric in France, where political parties in the country's hung parliament are wrangling over a draft law governing new arrivals.
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Interior Minister Gerald Darmanin declared that France would not welcome any migrants coming from Lampedusa, after 8,500 people landed on the island over the course of three days.
There was also a diplomatic spat last November, when Ms Meloni's newly elected hard-right government refused to allow a migrant rescue ship to dock in Italy.
Paris eventually allowed the Ocean Viking ship into a French port, but denounced Rome's “unacceptable” behaviour and suspended plans to receive 3,500 migrants from Italy.
In recent days, both Paris and Rome have sought to ease tension.
“We cannot leave the Italians alone,” Mr Macron said in a television interview on Sunday – an offer of help that Ms Meloni immediately said she “welcomed with great interest”.
Italian Foreign Minister Antonio Tajani was in Paris on Monday evening for talks with his French counterpart.
Migration “is a problem that should be dealt with on the European level”, Mr Tajani said, and even called on the UN to intervene.
Ms Meloni has also clashed over migration with Germany, whose President, Frank-Walter Steinmeier, was also among those attending Mr Napolitano's funeral.
She wrote to Chancellor Olaf Scholz at the weekend to complain about Berlin's funding of charity projects to help migrants at sea and onshore in Italy.
Rome blames the NGO boats that conduct rescue missions in the central Mediterranean – the world's deadliest sea crossing for migrants – for encouraging arrivals from North Africa.
Data shows the boats do not work as a so-called pull factor, with departures instead strongly linked to the weather, while the vast majority of migrants are rescued by the Italian coastguard, according to the Interior Ministry.