The European Commission said on Monday it was confident that EU leaders could agree at a summit next week on handling migrants and refugees, but some diplomats were much less optimistic.
Migration has shot back to the top of Europe's political agenda after a junior coalition partner of German Chancellor Angela Merkel gave her until after the June 28-29 EU summit to get a deal with the other 27 member states.
The issue has divided EU states bitterly since arrivals from the Middle East and Africa shot up in 2014, with frontline countries such as Italy and Greece demanding their peers do more to help them handle people fleeing wars and poverty.
Germany, which has admitted more than 1.6 million people since 2014, also wants EU-wide solidarity, standing with other wealthy destination countries such as France and Sweden in demanding all EU states host some of those people arriving.
But ex-communist states on the EU's eastern flank led by Poland and Hungary refuse to let the mainly Muslim migrants in, citing security risks after a flurry of Islamist attacks in Europe, as well as the homogeneous make-up of their societies.
"Only a European solution and a European agreement can address this issue," a spokesman for the EU's executive European Commission, Margaritis Schinas, told a news conference.
"We are very confident that we have on the table all the elements that would facilitate an agreement in the European Council," he said of the upcoming meeting of EU leaders.
Schinas said the head of the Commission, Jean-Claude Juncker, would discuss the matter with Merkel and French President Emmanuel Macron on Tuesday.
German Interior Minister Horst Seehofer - the head of Merkel's governing partner, the Christian Social Union - said he would apply a unilateral ban on refugees who have already registered in other EU states if the summit brings no fix.
After three years of escalating feuds, national diplomats in Brussels have most recently been discussing another compromise proposal to let reluctant capitals avoid taking in a quarter of their "fair share" of asylum-seekers who make it to Europe.
Instead they would be allowed to bring in a handpicked person from across the Mediterranean or offer 30,000 euros to an EU host for each individual they refuse.
But Poland and Hungary said that still amounted to an unacceptable obligation, while Italy and Greece said it fell well short of what would be needed to alleviate their burden.
"A deal on migrants at the coming EU summit is unlikely," one diplomat said.
However, Schinas hinted that the EU could go for a majority vote to overcome the easterners' reluctance - something that is legally and technically possible but politically very sensitive.
Unable to clinch a deal within its ranks, the EU has increasingly tried to tighten its external borders and asylum rules in recent years, a line advocated by the bloc's current chair Bulgaria and by Austria, which takes over on July 1.
While the strategy has lowered immigration, Bulgaria's Prime Minister Boiko Borissov said separately in Sofia on Monday he would now push for "the closing of all European borders" to illegal migrants.
Data released on Monday by the EU's border agency Frontex showed some 43,000 people arrived in Europe between January and May, about half of the figure for the same period in 2017. The bloc's asylum agency EASO said that meant fewer asylum seekers.
Frontex has said, however, the western Mediterranean crossing has seen double the traffic so far this year compared to last, with some 3,400 people reaching Spain in May.
The EU's deals with Turkey and Libya preventing people from setting sail to Europe led to the big overall decrease. But these deals have been heavily criticised by human rights groups for exacerbating the suffering of people already in distress.