The summit, being held in Italy's ornate Senate, will last all day, with Italian ministers due to outline an array of initiatives, from energy and infrastructure to health and education, that Meloni says will be mutually beneficial.
"We believe it is possible to envision and write a new chapter in the history of our relationship, a cooperation among equals, far from any predatory imposition or charitable stance towards Africa," Meloni said in an opening speech.
She said the initiative would have an initial endowment of more than 5.5 billion euros ($5.95 billion), including public guarantees for investment projects and 3 billion euros from an international climate fund set up in 2021.
However, critics say heavily indebted Italy cannot hope to compete with the likes of China, Russia and Gulf states, that are all looking to boost their presence in Africa, which is home to many of the world's natural resources.
While Rome claims ownership of the plan, which it has named after the late Enrico Mattei, who founded state oil company Eni, Meloni said her government would look to help from the private sector and international bodies such as the European Union.
Underscoring that point, European Commission President Ursula von der Leyen, European Council President Charles Michel and the head of the EU Parliament were all at the Rome meeting.
Among the African leaders present were the presidents of Tunisia, Senegal, Kenya, the Republic of Congo and Somalia. In all, 45 African states were represented at various levels.
Meloni has made the Mattei plan a central plank of her foreign policy since taking office in late 2022.
Energy needs lie at the heart of the initiative, with Rome looking to serve as a gateway into European markets for natural gas from Africa that has become vital after Russia's invasion of Ukraine made diversification of supplies a priority for the EU.
Eni, Italy's largest importer of natural gas, has already countered lower Russian supplies by shipping increased volumes from Africa, where it has had a presence for decades. The company has said Algeria, Egypt and Libya will be Italy's main gas suppliers for the next few years.
But the Italian leader has repeatedly said Europe must forge closer ties across industry and agriculture, looking to strengthen African economies as a way of persuading disaffected young Africans from migrating north.
Some 157,600 boat migrants reached Italy last year, the largest number since 2016, undermining Meloni's electoral pledge to halt the flow of unauthorized arrivals.
Most had departed from North African countries such as Tunisia and Libya, many fleeing poverty and conflict in sub-Saharan Africa and the Middle East.
"Mass immigration will never be stopped, human traffickers will never be defeated if we do not address the many causes that push a person to leave their home," Meloni told the summit. "This is exactly what we intend to do."
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