By Alastair Macdonald and Robin Emmott
BRUSSELS (Reuters) - European Union leaders faced a daunting list of crises as they began their summit on Thursday, notably migrants crowding in at their southern borders, Russia growling in the east, Britain's threat to quit and a desperate need to create jobs.
But a battle of wills between Greece and its creditors that threatens to disrupt the euro single currency looked set to take up part of the 24-hour Brussels summit, despite frustrated leaders' efforts to push the issue down to their weary finance ministers to solve.
Thursday evening's agenda centered on British Prime Minister David Cameron formally requesting EU reforms to precede a referendum on membership.
"Dinner was supposed to be Britain," one EU official said. "Now we may have Greece for dinner, and the UK for dessert."
Summit chairman Donald Tusk had tried to head off distractions by obliging government leaders to attend a special euro summit on Monday in a bid to prove to Greece's novice left-wing premier Alexis Tsipras that leaders would not prove a softer touch than their financiers.
But by Thursday, round-the-clock negotiations in Brussels had failed to close the gaps on a cash-for-reform deal and EU officials said that, despite not being on the formal agenda, summit time might have to be devoted to it.
Tusk himself said he had a "hunch" the Greek story would have a "happy end" but foresaw hours of talks. German Chancellor Angela Merkel said leaders did not want to get drawn into it.
Plunged into crisis by the global crash in 2008 and unable to devalue its way out of debt due to the euro, Greece is also an element in the complex, interlinked challenges facing the EU - "Grexit", "Brexit", Russia and migration. One analyst this week dubbed them the "Four Horsemen" circling the summit.
At a pre-summit meeting of conservative leaders including Merkel and Spanish Prime Minister Mariano Rajoy, frustration with the leftists in Athens was clear. Antonio Lopez-Isturiz, the group's general secretary, said that migration and Britain's threat to leave would be discussed "with whatever time we have left" after dealing with Greece.
One conservative official added: "There is a lot of frustration that this is using up an enormous amount of time and energy that should be dedicated to other very pressing issues."
Finance ministers, too, made no secret of their irritation with the Greek negotiating tactics over the past four months, as Tsipras tries to get a deal that squares with pledges made to voters when he was elected on an anti-austerity ticket.
Finnish Finance Minister Alexander Stubb said leaders had "wasted a lot of air miles" on meetings that had come to naught.
ECONOMY AND MIGRANTS BOTHER BRITONS
Even a fix for Greece will not end much of Europe's trouble.
Greece's economic problems are in part a version writ large of many of those in the euro zone, including other peripheral states bailed out in recent years but also Italy and even France.
The summit agenda includes discussion of new recommendations for making the euro zone more stable and dynamic and of efforts to take advantage of new digital services across an EU market of half a billion people.
But those are now likely to get scant attention.
Economic drift in Europe and a fear of seeing Britain's economy being damaged by EU rules set for the German-led euro zone are among the reasons why Cameron has promised Britons a referendum by 2017 on quitting the bloc unless he can renegotiate terms.
So, too, is immigration, with open borders in Europe raising public concerns that link Africans and people from the Middle East risking their lives to cross the Mediterranean with migration to the west from the EU's poor, ex-Communist east.
Cameron may do little more than formally launch his request for a renegotiation, and hear little back other than an echo of Tusk's warning that fundamental EU principles -- notably free movement for workers -- are not to be bargained with.
The migration issue, partly driven by unemployment in the south of the euro zone, partly by troubles in Libya and the Middle East following Western backing for the Arab Spring, also affects Greece. Tusk is seeking backing for a plan to distribute 40,000 Syrian and Eritrean refugees from Greece and Italy around other EU states, though many have already dismissed the proposal.
This month has seen physical and diplomatic confrontations at the Italian-French border, at the Channel Tunnel linking France and Britain, and between Hungary and Austria as governments try to control the flow of migrants.
Some accuse Italy, and especially struggling Greece, of failing to monitor Mediterranean migrants arriving on their shores and instead turning a blind eye as they move on north.
One Greek minister last month threatened to "flood" Europe with migrants by ending attempts to stop them.
Others in the Athens administration have cautioned that a bankrupt Greece could turn to its old Orthodox ally Moscow for help -- worrying other NATO members, not least the United States, as it also frets over its Atlantic partner Britain turning its back on Europe.
Having driven EU leaders into a fragile unity on trade sanctions that are hurting their own economies to punish Russia for its moves on Ukraine, Moscow is also complicating the EU's response to the migrant crisis by denying it U.N. support for more aggressive military action against Libyan people-smugglers.
EU governments rolled over sanctions this week until January, sparing the summit a discussion of Russia. But deep divisions remain between those who want a hard line, whatever the cost in terms of cold war, and others who fear backing Russia into an isolation that could raise risks of conflict.
Rem Korteweg of the Centre for European Reform said: "Four horsemen ... are circling together and affecting each other.
"They raise issues that can only be solved if governments prioritize a European solution over narrow national agendas. If a European answer cannot be found, the horsemen will continue to promote chaos, instability and mutual recrimination."
(Additional reporting by Paul Taylor, Guy Faulconbridge and Philip Blenkinsop; Editing by Kevin Liffey)