With 80,000 refugees reaching Italy just this year, the country is warning it cannot cope and has threatened to close its ports to rescue boats.
Italy wants other European Union countries to do more to help it deal with the influx.
In the last three years, more than half a million migrants and refugees have arrived on Italy's shores.
It is still a growing issue, with 20 per cent more asylum seekers arriving this year than at the same time last year.
And just in the past week alone, more than 12,000 have made the perilous journey on boat.
The most recent arrived on a boat carrying 400 people, including women and children, mostly from sub-Saharan Africa and Bangladesh.
Italy says it is unsustainable and it may have to close ports and impound rescue ships run by aid agencies helping the migrants and refugees.
Interior Minister Marco Minniti says the process is not working if the only ports taking in people are Italian.
"It's not possible not to understand that something is not working if we have vessels coming in from all European countries, flying various European flags, sailing in the Mediterranean Sea, with (rescuers) rightly rescuing human lives, and, nevertheless, the only ports where these rescued lives are brought to are Italian ports."
Key EU leaders from Germany, France and Italy are meeting in Paris to discuss the options going forward and a coordinated response to the crisis.
But the talks are unlikely to lead to any concrete decisions because EU interior ministers are scheduled to meet next week in Estonia.
Italy does have the support of the European Union, which agrees the country can no longer handle the flood of migrants and refugees alone.
EU commissioner for migration Dimitris Avramopoulos says he believes Italy is right that the situation is untenable.
"Italy has to adopt the measures to speed up the procedures and to manage migrants on its territory. We are ready to increase our support to Italy, including substantial financial support if needed. All member states now need to deliver and show solidarity towards Italy."
But three European countries refusing to share the burden are Hungary, Poland and the Czech Republic.
Poland's most powerful politician, Jaroslaw Kaczynski, from the ruling Law and Justice party, argues his country has a right to reject refugees.
"We did not exploit those countries from which the refugees come to Europe today. We did not exploit their labor force, and, finally, we did not call them to come to Europe. We have a full moral right to say no."
But as the leaders talk, the situation is becoming grim.
Ewa Moncure, from the European border-management agency Frontex, says more and more people are dying because of overloaded boats.
"The presence of the rescue boats, the smugglers are aware of the rescue boats, and they are taking advantage of it in the sense that we are seeing more and more people per boat. So two years ago, you would see a rubber dinghy, and there would be 90 people on the rubber dinghy. And, of course, it's a terribly dangerous situation, a rubber dinghy with 90 people on board. Today, you see the same rubber dinghy with 150, and sometimes even 180, people."