Interior Minister Gerald Darmanin said Italy faced a "very serious migration crisis" and he drew parallels between Meloni and French far-right leader Marine Le Pen.
"Madame Meloni, a far-right government chosen by friends of Mme. Marine Le Pen, is incapable of resolving the migration problems on the back of which she was elected," Darmanin told RMC radio.
Asked about the arrival of migrants at France's southeastern border with Italy, Darmanin said there was "an influx of migrating people and particularly children."
His statements came the same day as Italian Foreign Minister Antonio Tajani was visiting Paris for talks with his French counterpart Catherine Colonna.
The centrist French government under President Emmanuel Macron has clashed repeatedly with far-right Italian cabinets in recent years over migration.
The most recent spike in tensions came last November when Meloni refused to allow a humanitarian ship carrying 230 migrants to dock in Italy.
The ship was allowed to dock in France, but Paris denounced Rome's "unacceptable" behavior and suspended plans to receive 3,500 migrants from Italy.
At the time, Meloni denounced France's reaction as "aggressive" and "unjustified."
Relations have since improved, with Macron and Meloni meeting in Brussels in March for talks.
France: Italy PM 'Incapable' of Fixing Migrant Crisis
FILE: Migrants associations members show banners reading in Italian "All brothers, we want peace because we know war, residence permit" during a protest against Italy's government's migrants' policy in Rome, Tues. April 18, 2023.
PARIS - Italy's Prime Minister Giorgia Meloni "is incapable of resolving the migration problems" faced by her country, France's interior minister said Thursday in comments that risk fueling tensions between Paris and Rome.