* EU puts majority vote on the table if no deal by June
* Bloc as split as ever on obligatory relocation quotas
* East EU states oppose hosting refugees (Updates with fresh quotes, colour)
By Gabriela Baczynska and Robert Muller
BRUSSELS, Dec 15 (Reuters) - European Union leaders appealed for unity in a last-ditch effort to break their deadlock on sharing out refugees by June, telling reluctant eastern states they could otherwise be outvoted on a dispute that has shaken the bloc's foundations.
Coming out from a fraught discussion among 28 EU leaders that went into the small hours on Friday morning in Brussels, rivals in the two-year-old dispute all stuck to their guns, hemmed in by expectations they have raised with their own voters.
The Mediterranean frontline states Italy and Greece, and the rich destination countries including Germany, Sweden, Belgium, France, Luxembourg and the Netherlands are demanding that all countries host some refugees as a way to demonstrate solidarity.
Their four ex-communist peers Poland, Slovakia, Hungary and the Czech Republic refuse to accept people from the mostly-Muslim Middle East and North Africa, saying that would threaten their security after a raft of Islamic attacks in Europe.
"There are areas where there is no solidarity and this is something I find unacceptable," German Chancellor Angela Merkel told reporters.
At one point during the two days of talks in Brussels, cameras caught Merkel, the bloc's paramount national leader, as she appeared to become agitated when talking with the leaders' chairman, Donald Tusk, making her displeasure with him clear.
That came after Tusk, a former prime minister of Poland, came out strongly against "ineffective" and "highly divisive" obligatory refugee quotas, ruffling the feathers of those states that back them as well as the executive European Commission.
"The manner in which the principle of solidarity was being questioned does not only undermine the discussion on the refugee issue, but the future of Europe," Greek Prime Minister Alexis Tsipras told reporters after what he called "intense" talks.
Tusk said the ineffectiveness of relocation schemes was demonstrated by the fact that only 35,000 asylum seekers had been transferred from Greece and Italy under a 2015 plan meant to move 160,000 people.
"Mandatory quotas remain a contentious issue," Tusk told a joint news conference with the Commission's head Jean-Claude Juncker, the disagreement between the two playing out visibly despite their usually friendly rapport. "Relocation is not a solution to the issue of illegal migration."
"Will a compromise be possible? It appears very hard. But we have to try our very best," he said, stressing the bloc was in full agreement about making further efforts to tighten its borders and chip in for development and migration-related projects in the Middle East and Africa.
After sealing a deal with Ankara in 2016 that cut off arrivals from Turkey to EU state Greece, the bloc is now pushing to stem African immigration to Italy through Libya.
Tusk, Dutch Prime Minister Mark Rutte and other leaders said they wanted to make permanent financing available for such activities in the bloc's next long-term budget from 2021.
But it is the feud over how to share the burden of caring for those refugees who still make it to Europe that has weakened the bloc's cohesion and undermined member states' trust in each other at a time they need unity to face Brexit.
After many months of letting the open wound fester, the backers of quotas made clear they want to move on and would vote on the broader reform of the bloc's asylum system by majority if no compromise acceptable for all is found by June on relocation.
"I am not a fan of qualified majority decision-taking but... it can be used," Juncker said. "Some of our colleagues were openly saying yesterday night that if there is no progress, they will propose qualified majority decision-making procedure."
That would inevitably deepen divisions in the EU and the four eastern states warned that the bloc would shoot itself in the foot should it go down this track.
The only proposal the EU has on the table on asylum reform has most recently been updated by Estonia and attempts to bridge the divide by proposing that any relocation of asylum-seekers from one EU state to another, while obligatory at times of extremely high arrivals, would in fact only take place if both involved agreed voluntarily to the terms.
Diplomats in Brussels hoped Italy would be more willing to compromise after it holds elections, most likely in March, and said Germany could reassume the lead on the file after it forms a ruling coalition following an election last September.
A senior EU diplomat from one of the pro-quota countries said they would seek to break the united front of the four eastern states to bring down the number of countries that would eventually be defeated in a vote if everything else fails. (Additional reporting by Robert-Jan Bartunek, Francesco Guarascio, Jean-Baptiste Vey, Noah Barkin, Luke Baker, Alastair Macdonald and Michele Kambas; Editing by Andrew Heavens)
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