"I think it was better than expected, there was some progress that has been achieved", Maltese Prime Minister Joseph Muscat said, echoing a similar assessment by his Spanish counterpart, with both describing frank exchanges in the afternoon meeting.
Rounding out the 16 leaders, European Union officials said, are those from Austria, Greece, Malta, Bulgaria, Belgium, the Netherlands, Croatia, Slovenia, Denmark, Finland, Sweden and Luxembourg.
Sunday's mini-summit was called by European Commission President Jean-Claude Juncker who billed it as an "informal working meeting" in advance of an important EU summit on migration policy scheduled for June 28 and 29. Hungary, the Czech Republic, Poland and Slovakia announced a boycott of the meeting.
Sunday's mini-summit is supposed to prepare for a full summit next week, where 28 European Union leaders will discuss plans to overhaul the bloc's asylum system, which has been under severe pressure since the migration crisis exploded in 2015.
Chancellor Angela Merkel's long-time allies in Bavaria are on track for their worst ever performance in October elections, according to a poll on Monday, suggesting their harder line on immigration is failing to lure voters from the far right.
The 16 leaders - representing more than half of the 28-member European Union - are taking part in the informal talks that German Chancellor Angela Merkel said will involve "talking with particularly affected nations about all problems connected with migration".
Instead, she said, "bilateral, trilateral and multilateral" deals must be reached to tackle the issue.
Just three weeks in office, Italy's new populist government is digging its heels in on campaign promises to stop the influx of migrants, threatening to seize rescue ships or barring them from its ports.
Far-right Interior Minister Matteo Salvini also reacted furiously in remarks reported by Italian media.
The apparent progress Sunday on "secondary" migration movements, including those reaching Germany, may help ease the political pressure Merkel faces.
Prince William visits Jordan ruins where Kate played as child
The Jordanian crown prince recorded it for him, and the two watched it later Sunday on a huge TV screen at Hussein's residence. The comments came as Syrian government forces advanced in southern Syria, near Jordan's border, leading to more displacement.
The two leaders also said they support the creation of closed reception centers where migrants would be held as they asylum claims are considered.
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".
After turning away the Aquarius, which later docked in Spain, Rome vowed Saturday to block the Lifeline, a German charity vessel with more than 230 people aboard.
"In Italy, the immigration emergency.is also fueled by France with its constant rejections at the border".
United Nations refugee agency chief Filippo Grandi said last week that the migrant crisis can "be solved by cooperation, not country by country".
In this photo taken on Thursday, June 21, 2018, migrants on a rubber boat are being rescued by the ship operated by the German NGO Mission Lifeline in the Mediterranean Sea in front of the Libyan coast.
Spanish authorities said they had rescued almost 600 migrants trying to make the perilous crossing from Africa, while off the coast of Libya coastguards recovered bodies of five migrants and picked up 210 survivors, the coastguard said.
Under the so-called Dublin rules, asylum-seekers must be processed in the country where they first arrive, often Mediterranean countries like Italy, Greece and Spain.
The new Italian government has intensified existing Italian complaints that the country is taking in more than its fair share of refugees thanks to the number of people fleeing Africa by boat in recent months, many of them heading to Italy, one of the closest points in Europe to their starting point in Libya.
Macron also said France favoured financial sanctions for EUcountries that refuse migrants with proven asylum status.