Banking supervisors from the EU's 27 countries will wrap up a test of the entire EU-wide banking sector in September to check how resilient it is to new shocks. The test does not assess individual banks.
They said they have no plans to publish the results of that or a similar test they ran in May.
Some nations are also separately testing how well each bank could cope with problems and trying to identify which might need new cash injections to counter risks.
EU Economic and Monetary Affairs Commissioner Joaquin Almunia told reporters Tuesday that some EU governments want to see tests on individual banks run across the EU.
"Some countries consider that the stress testing ... should be better harmonized at the European level and should even be made public, as the Americans did," he said.
In the United States, the Federal Reserve tested the country's 19 biggest banks and told 10 of them - including Bank of America, Citigroup and Wells Fargo - to boost capital by a total of $75 billion to cover potential losses.
Britain has also conducted tests but released little detail, while Germany has argued that going public could undermine fragile economic confidence.
Almunia said the EU's executive commission could not call on national supervisors to make changes, but favored "the highest transparency possible" to regain confidence in the banking sector.
He called on banks in trouble to draw on liquidity offered by governments last October to help them overcome a credit freeze that has triggered a deep economic downturn.
"The capital pledges ... (have) not been used 100 percent. In some member states (they have) not been used at all," he said.