"Maybe not everyone is aware of the risks we are facing about the Tunisia situation and the need to support stability in a nation that has serious financial problems," she told reporters after the meeting of EU leaders, at which she said she raised the issue.
"If we do not address those problems in the right way, (the situation) risks unleashing a wave of migration which is objectively unprecedented," she said.
Meloni said she had discussed Tunisia with French President Emmanuel Macron during a bilateral meeting late Thursday, which she described as "very productive", after months of tensions between Rome and Paris over migration and other issues.
Meloni said she had also discussed the situation with EU Economy Commissioner Paolo Gentiloni, who she said would visit Tunisia in the coming days.
"Tunisia urgently needs aid. We cannot waste time", FM Tajani told RAI public radio.
Bailout talks between Tunisia and the International Monetary Fund (IMF) have been stalled for months, with the U.S., among others, demanding far-reaching reforms from President Kais Saied to free up the cash.
Tajani said he had proposed to fellow EU foreign ministers on Monday to split the bailout funds into instalments, with a first payment freed up immediately and later ones linked to progress on reforms.
"We risk having tens, maybe hundreds of thousands of people in the Mediterranean Sea who will be on the move ...," Tajani said.
Having received more than 20,000 boat migrants so far in 2023, Italy is on track to beat the all-time high for arrivals set in 2016, when 181,436 people reached the country mostly in flimsy boats.
Most are coming through North Africa from sub-Saharan Africa, but a senior official in Rome says the Italian government is worried that many Tunisians will be on the move, too, if their country's economy collapses.
According to United Nations data, at least 12,000 of those who have reached Italy this year set sail from Tunisia, against 1,300 in the same period of 2022.
On Thursday, a Tunisian judicial official said at least five migrants had died and another 33 were missing after four boats sank off Tunisia while trying to cross the Mediterranean to Italy.
