More European banks face stress tests to assess their health, officials acknowledged yesterday, amid warnings that publishing detailed test results for the continent's biggest financial institutions may not fully quell investor concerns.

European Union leaders have agreed to publish stress test results for 26 banks next month - an unprecedented attempt to restore market confidence battered by weeks of worry about high levels of eurozone sovereign debt. The euro, stock markets and some European bond markets rose yesterday in response to the agreement, but doubts persisted about the detail of the tests. Analysts were unsure whether results would be published bank-by-bank and how credible tests would be.

Concern also surrounds the health of Europe's large number of smaller banks that are not covered by stress tests. José Manuel Barroso, president of the European Commission, said in Florence yesterday that authorities would persist with bank stress tests involving "much more" than the 26 banks being examined by European regulators.

Germany was understood to have wanted to widen stress-testing to include other public-sector banks, seen as a weak link in its system.

But Germany said its laws meant it could not compel banks to reveal stress test results. It made clear it would rely on peer pressure to herd banks into line and to publish results.

There was also doubt about how the tests to be made public would deal with banks' holdings of European sovereign debt. That has been one trigger for the waning market confidence in banks, as concerns have intensified about the possibility of a default by a eurozone member.

The EU-wide stress test is not understood to have encompassed specifics about banks' sovereign debt exposure, but an assessment of sovereign risks "will be captured" in other ways, said one person involved in the process.

People close to the stress-testing process also suggested it was less draconian than tests conducted last year.

Ralf Preusser, the head of European rates research at BofA Merrill Lynch Global Research, said: "Publishing stress tests is a good thing - but we do need to know what they have actually stressed. Will they stress the possible outcome of a Greek default on [the country's] bonds, for example?"

Banks to be tested now were "not really the concerns", Mr Preusser said. "Concerns surround the second-tier institutions. We need information on these banks."

Huw van Steenis, analyst at Morgan Stanley, said: "If well executed, we think this is likely to help market confidence - although there are still plenty of open questions about how definitive these tests will be."

Regulators believe that such tests should help to calm investor concerns about bank risks. "Banks generally have very materially increased their capital versus their risk-weighted assets and the environment is much better than it was," said a senior European regulator.