* EU leaders agree youth unemployment fund, SME credit
* Summit follows breakthrough on bank resolution, EU budget
* Hitch over British rebate overcome, officials say
By Luke Baker and Paul Taylor
BRUSSELS, June 27 (Reuters) - European leaders agreed on new steps to fight youth unemployment and promote lending to credit-starved small business on Thursday after deals on banking resolution and the long-term EU budget gave their summit a much needed lift.
The 27 leaders resolved to spend 6 billion euros over the next two years to support job creation, training and apprenticeships for young people, and to raid unspent EU budget funds to keep the effort going thereafter.
Critics say the money is a drop in the ocean with more than 19 million people unemployed in the EU, and more than half of all young people under 25 without a job in Spain and Greece.
Leaders also approved plans for the European Investment Bank to lend hundreds of billions of euros to small and medium-sized enterprises (SMEs) particularly in southern EU states where bank finance has largely dried up due to the euro zone's debt crisis.
"The last 24 hours have been a great success," European Commission President Jose Manuel Barroso told a news conference. "Today we have agreed the money to back up our words."
After late-night talks in Luxembourg, European Union finance ministers agreed how to share the cost of future bank failures among investors and wealthy savers as far as possible.
Separately, negotiators for the European Parliament, the European Commission and EU member governments clinched a deal on a 960 billion euro ($1.25 trillion) seven-year budget for the bloc for the period 2014-20, ending months of squabbling.
The leaders unanimously endorsed the agreement, EU Council President Herman Van Rompuy said, overcoming a last minute snag over Britain's rebate, which will remain intact. The European Parliament must approve the deal next month so the new budget can take effect next January.
The banking resolution agreement designed to shield European taxpayers from having to foot the bill for rescuing troubled banks will be implemented on a national basis from 2018.
It lays the ground for a single system to resolve failed banks in the euro zone and the 27-nation EU, the second stage of what policymakers call a European banking union, meant to strengthen supervision and stability of the financial sector.
The European Commission, the EU's executive, will put forward proposals for a single resolution mechanism next week, but any deal on it is a long way off because EU paymaster Germany opposes taking any liability for other countries' banks.
German Chancellor Angela Merkel welcomed the EU budget breakthrough, saying it would allow new spending on everything from agriculture to research, roads, bridges and development aid to move ahead, promoting economic growth in Europe.
LOW GROWTH, NO JOB
With two major obstacles out of the way, EU leaders faced a far less awkward agenda during the two-day summit focused on unemployment, the most devastating legacy of the crisis that has bedevilled the EU since 2010.
The last summit before Germany's September general election - a key date in Europe's political calendar - was one of the least contentious of the past three years.
But Merkel, favourite in opinion polls to win a third term, denied widespread talk that key European decisions on crisis management, banking union and issues such as entry negotiations with Turkey and carbon emissions for cars were on hold until after the vote.
"I know of no issue on which a decision has not been taken because of the fact that we have elections in three months' time," she told reporters.
The calm summit mood was a far cry from the peak of the debt and economic turmoil of late 2011 and early-to-mid 2012, when there was a real threat of the euro zone collapsing.
Since then, thanks largely to a promise by the European Central Bank last July to do whatever it takes to defend the single currency, pressure from financial markets has eased and EU leaders have made some progress in reforming their economies.
As well as strict new rules on budget deficits and tighter oversight of budget spending plans by the European Commission, steps have been taken to improve banking supervision and weaken the link between indebted countries and problem banks.
From late next year, the European Central Bank will become the single supervisor for virtually all the euro zone's 6,000 banks - the first stage of banking union.
The next step, the creation of a single resolution mechanism, is likely to prove a deeply divisive and drawn out process, with sharp differences between the views of the EU institutions, Germany, France and other member states.
Further-reaching plans for a single bank deposit guarantee across the euro zone look unlikely to gain traction due to German and north European opposition, although officially the idea remains on the table.
Most of Europe has been either in recession or on the brink for the past three years, while unemployment has steadily risen. EU unemployment now stands at 11 percent, the highest since records began, with youth unemployment a particular problem, especially in Spain, Greece, Italy, Portugal and Cyprus.
The new EU fund will back a "youth employment initiative" that would offer people under 25 a promise of a job, training or apprenticeship within four months of leaving education or becoming unemployed.
Politicians and sociologists are worried that extended unemployment for young Europeans will lead to a "lost generation" that never gets fully incorporated into economic life, with deep psychological and financial implications.
That will even further undermine Europe's ability to boost growth and compete with the rest of the world, especially China and a United States that is shifting its focus to Asia.