The meeting in Rome brings together 20 countries, European Union officials and international organisations.
The one-day conference is a Meloni initiative that aims to make Italy a leader in resolving issues affecting Mediterranean countries.
Chief among them is migration, as Italy sustains hundreds of new arrivals daily on Europe's southern border, but also energy as Europe looks to Africa and the Middle East to permanently replace Russian supplies.
Human rights groups view the meeting, which includes countries from both northern and sub-Saharan Africa as well as the Middle East, as creating a future roadmap and worry it will amount to anti-migrant policies that put the onus on Africa to keep Africans out of Europe.
Meloni told the opening meeting that European arrogance had likely stood in the way of solutions to the migrant issue.
She proposed four main prongs for future co-operation: fighting criminal organisations trafficking migrants, better managing flows of migrants, supporting refugees and helping countries of origin.
"The West too often has given the impression of being more interested in giving lessons rather than lending a hand," Meloni said.
"It is probably this diffidence that has made it difficult to make progress on solutions."
She said if flows were better managed there would be more room for legal migration.
"In an era where so much attention is given to the right to migrate, we are not paying sufficient attention to the right to not be forced to emigrate, to not be forced to flee their own homes, to not be forced to abandon their land and leave family members in search of a new life."
The conference comes against the backdrop of migrants being pushed back from Tunisia into Libya, where they are stuck in the desert.
Pope Francis, in his traditional Sunday blessing, called on leaders in Europe and Africa to find a solution to the thousands of people who are blocked at borders in North Africa.
"Thousands of them have been experiencing indescribable suffering for weeks, and have been trapped and abandoned in deserts," the pontiff said.
"May the Mediterranean no longer be a theatre of death and inhumanity," the Pope said, calling for a sense of "fraternity, solidarity and welcoming".
The summit comes a week after one of the key participants, Tunisian President Kais Saied, signed a memorandum of understanding for a "comprehensive strategic partnership" in a meeting that included Meloni and EU Commission President Ursula von der Leyen.
Financial details were not released but the EU has held out the promise of nearly 1 billion euros ($A1.7 billion) to help restart Tunisia's hobbled economy and 100 million euros for border control as well as search and rescue missions at sea and repatriating immigrants without residence permits.
Migrants pay traffickers thousands of euros to make the perilous journey across Africa's deserts.
Many report suffering torture and other abuse along the way.
And hundreds drown each year at sea trying to reach Italy in fragile boats.
More than 1900 migrants have died or gone missing in the Mediterranean so far this year, bringing the total of dead and missing since 2014 to 27,675, according to the International Organisation for Migration.
A further 483 are dead or missing in Africa this year.
