One of the key accomplishments of the EU is the Schengen free travel zone and some fear that closing internal borders between EU nations to keep migrants out would undermine that cornerstone of EU co-operation. The U.N.'s refugee agency says that around 80,000 people are expected to arrive by sea this year, around half the number from 2017.
French President Emmanuel Macron said the leaders discussed closer cooperation with non-EU countries, such as transit countries, in managing migration flows, as well as secondary migration movements within the bloc. He mentioned Libya - the main jumping off point for countries bound for Europe - other African countries and the Balkans.
Sunday in Brussels will be an informal European Union summit on migration with the participation of 16 European Union member States, however, breakthrough it is not expected.
And Italy's new Government has unveiled a sweeping set of anti-immigration proposals that would more quickly send migrants back out of Europe.
"That's global law" she added.
The International Organization for Migration (IOM) and the UNHCR are cautious about setting up "hotspots" outside of Europe to filter people fleeing violence at home from those trying to get to the continent to improve their lives economically.
European Union leaders gather in Brussels today in an attempt to bridge their deep divisions over migration, an issue that has been splitting them for years and now poses a fresh threat to German Chancellor Angela Merkel.
With such reform elusive, Merkel is now pushing for bilateral, trilateral and multilateral deals.
But she said the Italian coastguard had told the group they "weren't needed" and "the operation was being handled by the Libyan coastguard". France's Macron also supported the idea of members acting in smaller groups.
Meeting his counterpart in Libya's government Abdulsalam Ashour and Deputy Prime Minister Ahmed Maiteeg, Salvini thanked the Libyan Coast Guard for its "excellent work" in rescuing and intercepting migrants.
Referring to hasty arrangements and a domestic crisis over migration policies within Merkel's coalition government, the fervently anti-migrant Hungarian prime minister, Viktor Orban, said: "We understand that countries have domestic political difficulties, but this can't result in pan-European confusion".
His appeal came as migration tensions surged on the Mediterranean itself.
A handout photo from the German NGO "Mission Lifeline" shows migrants onboard the Lifeline sea rescue boat at sea on Thursday.
Italy's new populist government has refused entry in recent days to two rescue ships with hundreds of people aboard.
"The Lifeline, an illegal ship with 239 immigrants on board is in Maltese waters", Italy's far-right Interior Minister Matteo Salvini wrote on Facebook.
Sunday, June 24, in Brussels will host an informal summit of several European Union countries, dedicated to solving the problem of refugees.
Arriving at the summit, Malta's prime minister, Joseph Muscat, sought to defuse the row, saying it was not a time for finger-pointing as he advised against "building a wall even on the high seas".
Diplomats from France, Spain, Italy and Malta held intense talks about each country taking in people from Lifeline.
As with everything linked to migration in Europe, even the meeting in Brussels did not please everybody.
Italy and Austria have joined the four Visegrad countries of Hungary, Poland, Slovakia and the Czech Republic, which boycotted the mini-summit, in attacking Brussels' handling of the crisis.