As 16 EU countries were to meet on the issue at a mini-summit in Brussels on Sunday, the German charity expressed hope other European countries may help out.
The EU's top migration official on Monday urged European nations to work together to solve the migration crisis, ahead of a key summit in Brussels.
Later, she gathered for a meeting in her Berlin office with her right-wing coalition partners to try to defuse the row on immigration that is threatening to topple her three-month old government, days before a crunch summit of European Union leaders who are also divided on the issue.
Echoing Merkel, he also raised the prospect of some member states acting alone, if it proved impossible to find agreement between all 28.
However, Merkel appeared resigned to pursuing bilateral migrant return agreements with individual countries rather than a common European solution.
But Rome has already rejected measures that could see it handle even more people and the Sunday talks are all but certain to see the two countries clash.
Speaking alongside Spanish Prime Minister Pedro Sanchez, Macron told a press conference "You can't have countries that massively benefit from the solidarity of the European Union and that massively voice their national selfishness when it comes to migrant issues". This would greatly reduce the pressure on Italy.
It means, among other measures, setting up global protection centres in African transit countries to assess asylum applications.
They are considering setting up centers overseas to decide on asylum requests there and send back those whose cases fail.
Sixteen EU states presented a united front on migration in Brussels on Sunday (24 June), but tensions remain, with no solutions on paper for how to deal with people seeking global protection, their movements inside Europe, or plans to prevent them from taking boats from Libya.
"But we will always have legitimate asylum seekers who are entitled to our help". They also need to agree on how to share the burden of migrants.
But the issue has in the meantime won and lost elections for politicians across the bloc from Italy to Hungary, with voters favoring those advocating a tougher stance on migration.
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".
Migrants mostly stay in arrival countries like Greece and Italy or wealthy Germany where they try start a new life.
"You can not have countries that massively benefit from the solidarity of the European Union and that massively voice their national selfishness when it comes to migrant issues", he added, in a clear hint to Hungary, Poland and the Czech Republic, which oppose the EU relocation scheme for asylum seekers. Now backed by Austria, they want to end any further discussion on rules for sharing them out across the bloc.
Bad blood from the deadlock has spilled over to other areas of cooperation, including talks on the EU's seven-year budget from 2021. That would have a knock-on effect on other European Union states, hit cross-border business and travel.
Austrian Chancellor Sebastian Kurz says his country will reintroduce controls on its border with Italy if Germany were to turn back migrants at its border to Austria.
"These boats can forget about reaching Italy, I want to stop the business of trafficking and mafia", said Salvini, whose country is on the frontline of the migrant crisis.
The hard-line interior minister in Italy's new populist government, Matteo Salvini, said it was appropriate for the Libyans to take charge of the rescue "without the NGO vessels interrupting and disturbing them".
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