* EU leaders set course on budget rules, policy coordination
* Leaders agree on more transparent stress tests
* Bank levy, financial transaction tax proposed
(Edits, adds IMF, sources on stress tests)
By Jan Strupczewski and Timothy Heritage
BRUSSELS, June 17 (Reuters) - The European Union agreed unexpectedly on Thursday to carry out more transparent checks of its top banks' financial health as part of measures to convince investors it can contain a euro zone debt crisis.
EU leaders also agreed broad guidelines for tougher budget rules and closer economic policy coordination at a one-day summit, and said countries should face stronger sanctions if they did not meet budget and debt targets.
Budget plans must be submitted to the EU executive for peer review before national parliaments, and the leaders said they would propose a financial transaction tax to the Group of 20 developed and developing countries at a summit on June 26-27.
Accord over more transparent "stress tests" for banks, to be published in the second half of July, was not expected and followed increasing pressure from financial markets for more openness.
"Today the European Council (of EU leaders) has rolled up its sleeves and shown we can act together when there is a joint political will by member states and the European institutions," European Commission President Jose Manuel Barroso said.
The EU, which represents more than 500 million people, agreed last month on a 500 billion euro ($617 billion) safety net to help struggling countries that use the euro and a 110 billion euro aid mechanism for heavily indebted Greece.
But it has struggled to allay concern that debt repayment problems that began in Greece will not spread to other countries in the 16-country euro zone, such as Spain.
One leader after another rallied behind Madrid, praising austerity plans it has announced to address its problems, and markets were boosted by a successful bond auction in Spain.
STRESS TESTS BANK-BY-BANK
Madrid had called for more open stress tests, hoping this would prove its banks' good health. Some countries, such as Germany, have been reluctant to publish the results for individual lenders that could lay bare unpleasant details.
The stress tests gauge a bank's ability to withstand economic shocks and are intended to help prevent any further global economic crises.
Bundesbank head Axel Weber said a new set of European bank stress tests was needed to include a broader swath of the banking industry and new scenarios such as the debt crisis.
The International Monetary Fund also backed calls for better information on European banks' exposure to sovereign debt, and the United States has prompted Europe to be more open over the results of its stress tests. An EU diplomat, who asked not to be named, said: "It will be bank-by-bank for the 25 biggest banks."
The other unexpected measure agreed by the EU leaders was a financial transaction tax. That had been discussed by Germany but causes unease in some member states such as Britain, whose capital, London, is Europe's largest financial centre.
They also agreed on a growth and job creation strategy for the next decade and on a European banking levy, even though other world economies have avoided this.
The EU leaders say they will go it alone with the bank levy, if necessary. It is intended to raise money to help battle future crises from institutions widely blamed for the global economic meltdown.
TIGHTER ECONOMIC GOVERNANCE
The leaders did not set out to secure formal agreement on how to deepen policy coordination, and the tougher budget rules will not be set in stone until after a task force reports back on reforms to defend the euro in October.
They broadly concur on the need for closer policy coordination, or "economic government", and for tighter financial regulation, but do not agree how to go about it.
Differences linger between German Chancellor Angela Merkel and French President Nicolas Sarkozy, despite agreement on some issues at talks on Monday.
Britain is also hostile to parts of the drive towards closer budget surveillance and says it will not allow its budget plans to be submitted to the European Commission for review before the national parliament.
But EU diplomats said a phrase in a summit statement saying such moves must take account of national budget procedures addressed British concerns and did not cross what Prime Minister David Cameron said were his "red lines".
"We of course always defend our national interests as others do, and our national red lines, but we know how important it is that there is in Europe growth and confidence and that, I think, is the most important issue on the agenda," said Cameron, attending his first EU summit.
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For more on the euro zone, double-click on (Additional reporting by John O'Donnell, David Brunnstrom, Luke Baker, Ilona Wissenbach, Marcin Grajewski and Justyna Pawlak; Editing by Dale Hudson and Robert Woodward)