European Union leaders moved toward agreement on Thursday on ways to strengthen budget discipline and economic policy coordination among the 27 member states to contain a euro zone debt crisis.

EU diplomats said the leaders were broadly in agreement at a one-day summit on proposals to present budget plans to the executive European Commission for assessment and to penalize countries that do not aim for budget balance.

They faced pressure from some states to agree a levy to raise money from banks blamed for the economic crisis and calls for the results of stress tests that check banks' financial health to be published. Divisions remained on both issues.

The EU, which represents more than 500 million people, has agreed 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 despite repeated denials, national leaders and the Commission have failed to allay concern that Spain will follow Greece by seeking financial help.

I think Europe is still in a fragile situation when it comes to public finances, Swedish Prime Minister Fredrik Reinfeldt said on arrival for the one-day summit in Brussels.

We need to show leadership and determination on Europe ... and coordinate the measures needed.

Such concerns prompted Commission President Jose Manuel Barroso to propose accelerating the presentation of proposals for changes to EU budget rules.

The proposals, to be outlined on June 30, will focus on early budget coordination, reducing debt and more sanctions for rule breakers, and will offer details on ways to ensure EU budget rules are reflected in national law, EU sources said.

The Commission will further fast-track its work on economic governance, one EU envoy said.

SHOW OF UNITY

A show of unity was likely at the summit, which was reviewing the findings of a task force set up to look at reforms designed to prevent debt building up, increase cooperation and set up a permanent aid mechanism for countries in debt trouble.

The leaders were not seeking a formal agreement on how to deepen policy coordination, but any sign of divisions could increase the market nervousness that has helped drive down the euro and shares globally this year.

Luxembourg Prime Minister Jean-Claude Juncker, who heads the Eurogroup of finance ministers from the 16 EU countries that use the euro, acknowledged in a newspaper interview that Spain faced problems.

But he said Madrid would not be a specific item on the leaders' agenda, and financial markets were boosted by a successful bond auction in Spain.

EU leaders 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, who lead the euro zone's biggest economies, despite agreement on some issues at talks on Monday.

Britain is hostile to parts of the drive toward 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.

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, British Prime Minister David Cameron said, attending his first EU summit.

STRESS TESTS AND BANK LEVY

The leaders were pressing on with discussion of moves toward a European banking levy after the world's top economies failed to agree on such a tax for an industry widely blamed for the global economic meltdown.

They aim to agree a joint position for the G20 summit in Toronto on June 26-27. Merkel appealed to the other leaders to back the bank levy but divisions remain over how any measures should be implemented.

Pressure is also mounting for European regulators to publish results of stress tests on individual banks to restore market confidence and overcome a partial freeze in interbank lending.

Some countries, such as Germany, are reluctant to publish the results of stress tests for individual lenders that could lay bare unpleasant details about their financial health.

An EU source said the results of stress tests being carried out on European banks would not be published before the beginning of July.

We have been asking for increased transparency all the time ... but I know that there are some differences in the positions sometimes regarding this, Sweden's Reinfeldt said.

(Additional reporting by John O'Donnell, David Brunnstrom, Luke Baker, Ilona Wissenbach, Marcin Grajewski and Justyna Pawlak; Editing by Dale Hudson)