"We are studying new solutions and I will be able to announce important news as soon as Monday," Di Maio wrote in a Facebook post after "four very intense days" at the United Nations General Assembly in New York.
"Steps forwards were also made on the war in Libya, which is not just about a devastating conflict but is also linked to migration flows," he wrote.
There was also agreement in New York on the urgency of stopping the people smugglers, repatriating failed asylum-seekers from Europe, and revising the European Union's Dublin Regulation which forces migrants to claim asylum in the first EU country they arrive in, Di Maio wrote.
"As the moment, this (the Dublin Regulation) requires Italy to take in all the migrants who reach our country," read the post.
In view of the well-documented allegations of violence that migrants endure while transiting Libya, Italy "proposed that the UN run the chaos-stricken country's migrant reception centres," Di Maio wrote.
The almost six-month-old battle for Tripoli between eastern warlord Khalifa Haftar's forces and militias allied to the internationally recognised government has driven at least 120,000 people from their homes and killed well over a 1,000 people, among them more than 100 civil, the UN says.
Libya - an oil-rich former Italian colony - has been in turmoil since the Nato backed ouster of late dictator Muammar Gaddafi in 2011. The protracted lawlessness has enabled traffickers to flourish and extremist groups to gain foothold in the North African country.
/AKI
( With inputs from IANS )