U.S. banks undergoing stress tests that need more capital will be encouraged to first go to their current stakeholders, possibly through conversions of preferred stakes to common equity, Federal Deposit Insurance Corp Chairman Sheila Bair said on Friday.

Bair said any banks deemed to need more capital under the tests for more adverse economic conditions should extend conversion offers to their current shareholders before seeking government funds.

They just need to make some hard decisions and there should be some fair terms in the conversion offers, Bair said at the Reuters Global Financial Regulation Summit in Washington. Nobody wants the government money right now so that might be a good lever.

She does not foresee administration officials having to ask Congress for more financial bailout funds after the stress test results are released on May 4.

The U.S. Treasury Department has about $100 billion left in the $700 billion financial rescue fund. Policymakers have said the banks will have six months after the stress tests to raise private capital if more is needed, or they will have access to more government capital.

Bair also said the FDIC plans to meet in late May to reduce its proposed emergency assessment fee on banks to as low as single digits from 20 basis points.

The FDIC proposed the emergency fee -- scheduled to be collected in the third quarter -- to replenish its deposit insurance fund, which has been dwindling due to a sharp upswing in bank failures. The bank industry has said the one-time fee would cost as much as $15 billion at a time when the institutions can least afford it.

Regarding any stress test banks that need more capital, Bair said regulators can talk with those institutions on how to structure conversion offers to their current shareholders.

Regulators have stress tested the largest 19 U.S. banks to see how they would fare if the recession proves to be deeper than expected.

Officials are due to release later on Friday a document that will describe in detail the bank regulators' method of evaluation, including the underlying concepts and variables. The results of the stress tests will be announced on May 4.

Bair said policymakers are still discussing how to release those results. She would not say if results from individual institutions will be disclosed.

(For summit blog: http://blogs.reuters.com/summits/)

(Reporting by Karey Wutkowski; editing by Tim Dobbyn)