The U.S. Treasury Department is facing mounting pressure to ensure that taxpayers get a fair return on banks' warrants as the largest firms prepare to shake off government ownership stakes.

At the same time, Treasury is mired in negotiations with the banks, who want to lower the warrants' multi-billion dollar price tag and avoid another big hit to their capital position.

The pricing of the warrants held by Treasury ... will be critical to ensuring an appropriate return on investment for the government and, consequently, American taxpayers, the two chief watchdogs of the financial rescue wrote this week in a letter obtained by Reuters.

A financial industry source said banks' negotiations with Treasury over the value of the warrants are calm but said the price ranges are all over the place.

The debate over the warrants is coming to a head as next week 10 of the biggest banks will begin to repay almost $70 billion in Troubled Asset Relief Program (TARP) funds, freeing the firms of a public stigma and restrictions on executive pay.

Repaying rescue funds will involve banks buying back the preferred shares that many sold to the government when financial markets were squeezed by a credit crunch last fall. But banks also wish to repurchase the warrants that give the government the right to buy common stock at a pre-set price for up to 10 years.

Some big banks, including JPMorgan Chase & Co , argue they should get a discount on the warrants because they did not want the money in the first place. Lawmakers say Treasury should give taxpayers their fair share of the gains in the banks' stock prices.

We will be working with the government on the timing and valuation of all payments, Ron Gruendl, a spokesman for Bank of New York Mellon , told Reuters.

Bank of New Mellon is on the list of banks green lighted earlier this week to exit TARP. Others include American Express , BB&T , Goldman Sachs , JPMorgan, Morgan Stanley , and U.S. Bancorp .

As negotiations continue, Treasury is facing more scrutiny from the two primary TARP watchdogs have begun a project to estimate a reasonable range of values for the warrants.

In a letter dated Wednesday to leading lawmakers on the House and Senate financial committees, Neil Barofsky, the TARP special inspector general, and Elizabeth Warren, the chairwoman of the Congressional oversight panel for TARP, said they will work together to ensure taxpayers get a good return.

The project will also include an audit of the warrant repurchase process, they said.

WHAT IS FAIR VALUE?

Treasury has said it will sell back the warrants at fair market value but experts say pricing can be difficult since the investments are unique in the marketplace. That means banks can negotiate on the buyback price.

We are in the process of going through a judgment about what fair market value for those warrants is likely to be, Treasury Secretary Timothy Geithner told a Senate panel on Tuesday. Some of the estimates now are in the several billion dollar range for those initial banks that are repaying.

Treasury is facing pressure from lawmakers who want to make sure taxpayers see the upside promised to them when the government made the investments last October.

On Tuesday, Jack Reed, a leading Democrat on the Senate Banking Committee, discussed the warrants issue with Geithner and urged him to make sure taxpayers are paid their due.

But the banks want to get a good deal, especially after paying billions of dollars in dividends to the government.

The ten banks that have won the right to return their warrants have paid the Treasury about $1.8 billion over the past seven months, according to official data. In all, finance companies that have gotten government investments have paid about $4.5 billion to the Treasury.

Bank of America Securities-Merrill Lynch Research said on Friday that repayment of federal funds by Goldman Sachs, JPMorgan and Morgan Stanley will force a reversal of value for the remaining warrants. The analysts cut second-quarter profit estimates for the big U.S. banks.

While the firms should generate more than ample income to absorb the adjustment related to the main TARP payback, the warrant-related hit to capital is unavoidable, analyst Guy Moszkowski said in a note to clients.

The banks do have the option of exiting TARP by buying back the preferred shares, and letting Treasury liquidate the warrants.

But the banks won't want to dilute their current shareholders and keep the fingerprints of government on their financial reports, said Wayne Abernathy, executive director for financial institutions policy at American Bankers Association.

They don't want a lingering reminder that they were under a government program, Abernathy said.

(Reporting by Karey Wutkowski and Patrick Rucker with additional reporting by Anurag Kotoky in Bangalore, editing by Gerald E. McCormick, Bernard Orr)