The Visegrad Four (V4), a loose alliance of the Czech Republic, Hungary, Poland and Slovakia, do not want to host asylum seekers under any European Union plan, while Greece and Italy want a better distribution of asylum seekers, backed by Germany.
Sixteen of the EU's 28 leaders held talks in Brussels on Sunday, ahead of a summit, the European Council, on June 28-29. Hungary, the Czech Republic, Poland and Slovakia announced a boycott of the meeting.
As tensions rise between Rome and Paris as well as Rome and Berlin, the top-level talks are created to help clear the heavy air for a previously scheduled full summit of all European Union leaders on Thursday and Friday.
German Chancellor Angela Merkel said the meeting involves "talking with particularly affected nations about all problems connected with migration".
Merkel, who is scrambling to prevent a mutiny in her government over migration, admitted there were still "some differences" but also "a great deal of common ground".
"We cannot have countries that benefit hugely from European Union solidarity and claim national self-interest when it comes to the issue of migrants", he said at a press conference in Paris alongside Spain's new Prime Minister Pedro Sanchez.
Italy's transport minister accused Malta of an "inhumane" and "absurd" decision for refusing to accept the vessel, but Malta maintains that the ship is under Italian jurisdiction.
"The immigration emergency continues in Italy, partly because France keeps pushing back people at the border", Italian deputy prime minister Luigi Di Maio shot back on his Facebook page, warning Macron risked turning France into "Italy's number one enemy" on the issue.
Reactions to Merkel's failure to secure a deal varied but Malte Pieper, a correspondent with German public broadcaster ARD, felt so strongly about the failure she called on Ms Merkel to resign saying: "Clear the Chancellery for a successor whose name is not as loaded as yours is".
The leaders of several more countries joined Italy and France in endorsing the idea of setting up centers in Africa to screen potential asylum-seekers for eligibility before they set out for another continent.
German Chancellor Angela Merkel's coalition parties described their row on migrant policy as very serious after four hours of crisis talks on Tuesday night failed to defuse a dispute that threatens to tear apart her three-month old government.
Nobody at the summit accepted Merkel's proposal that willing member states form separate agreements where EU-wide consensus isn't possible, instead insisting on a European solution, according to an EU government official familiar with the discussion.
Amid the flurry of diplomacy, the rescue ship of German aid group Mission Lifeline remained stranded Sunday off Malta with 234 migrants aboard and no port at which to dock after both Italy and Malta refused to give authorization. According to Mission Lifeline, who rescued 224 migrants at sea, they are still seeking a port of destination.
Migrants mostly stay in arrival countries like Greece and Italy or wealthy Germany where they try start a new life.
Before the meeting had even begun, divisions were on display, as Italy and Malta traded insults over which nation was responsible for a boat of 234 migrants adrift in worldwide waters.
Northern countries, including Germany, want to limit "secondary movements" of protection seekers from the south, where they initially apply for asylum, to the more affluent states of the European core.
And Italy's new Government has unveiled a sweeping set of anti-immigration proposals that would more quickly send migrants back out of Europe. Failing that, he vowed to turn back migrants at the border, which means many will likely have to return to Italy under the so-called Dublin regulations.