The adverse scenario used to test the health of the 19 largest U.S. banks is disturbingly close to current economic conditions, sparking a concern that there might need to be a second stress test, a U.S. financial bailout fund watchdog said on Monday.

Elizabeth Warren, who chairs the Congressional Oversight Panel for the Troubled Asset Relief Program, said the test may in actuality be rigorous, but the government's recent document describing the test's methodology lacked critical details.

I had believed that we would receive a much more detailed description of the stress tests last Friday, Warren told the Reuters Global Financial Regulation Summit.

She said, ideally, the document released by the Federal Reserve on Friday would have provided enough detail to allow outsiders to run their own version of the stress test on the largest banks. The government plans to release the results of the tests on May 4.

Warren also said the public needs details on how rigorous the stress tests really were because the macroeconomic assumptions involving unemployment were not that much more severe than current conditions.

It looks disturbingly close to where we are now, Warren said.

The stress test aims to determine how much extra capital a bank might need if the economy deteriorates even further.

Regarding the disclosure of the test results, Warren said it is appropriately Treasury's decision whether to release the results of individual institutions.

However, Warren said the markets have already built steep discounts into the stocks of the major banks because investors fear the unknown. She said disclosing information about the banks' health could be helpful because markets will eventually uncover the banks' potential losses and capital needs.

I think ultimately the markets' reactions are positive in the sense that they will be both accurate and less weighed down by the fear of what is as yet undisclosed, Warren said. I truly believe you can't fool markets over any period of time.

But in order for the stress tests to be taken seriously, Warren said the government needs to prove they were robust.

The stress tests will make a terrific contribution if they are tough and transparent, Warren said. If they are not, they will be useless.

Warren said there is a concern that the government would have to conduct another stress test if the economy in the next few months hits the conditions outlined in the adverse economic scenario.

(Reporting by Karey Wutkowski; Editing by Tim Dobbyn and Carol Bishopric)