Updated from Monday, June 8

Federal regulators gave their blessing to capital-raising plans for the 10 banks ordered to bolster their balance sheets after government stress tests completed last month.

The brief announcement from the

Federal Reserve

said supervisors of the Supervisory Capital Assessment Program will work with the banks to ensure the plans are put into place "quickly and effectively." It was silent about whether regulators would give the green light to several banks that were not required to raise capital and had applied to repay federal investments made through the Troubled Asset Relief Program.

"The 10 banking organizations required by the

program to bolster their capital buffers have all submitted capital plans that, if implemented, would provide sufficient capital to meet the required buffer under the assessment's more-adverse scenario," the two-paragraph statement late Monday from the Fed said.

Results of government stress tests at the biggest 19 banks determined that 10 of them would need to raise nearly $75 billion in additional funds to prepare for a worst-case economic scenario. But even the weakest banks have had

surprising ease in

raising capital, and many have exceeded individual targets.

The excess cash is expected to go toward paying back funds from the Troubled Asset Relief Program, which nine banks have applied to do, and several others have expressed interest in doing as soon as possible.

Those that have applied to redeem the TARP investment are

JPMorgan Chase

(JPM) - Get Report

,

Goldman Sachs

(GS) - Get Report

,

Morgan Stanley

(MS) - Get Report

,

American Express

(AXP) - Get Report

,

BB&T

(BBT) - Get Report

,

State Street

(STT) - Get Report

,

Northern Trust

(NTRS) - Get Report

and

HF Financial Corp.

(HFFC)

.

Others that have indicated interest in paying back funds include

Bank of America

(BAC) - Get Report

,

Wells Fargo

(WFC) - Get Report

,

Fifth Third

(FITB) - Get Report

,

Bank of New York Mellon

(BK) - Get Report

,

PNC Financial Services

(PNC) - Get Report

,

KeyCorp

(KEY) - Get Report

,

Capital One

(COF) - Get Report

,

US Bancorp

(USB) - Get Report

and

SunTrust

(STI) - Get Report

.

Citigroup

(C) - Get Report

is not expected to redeem its government investment any time soon, nor is

General Motors'

GMAC subsidiary, since the automaker has filed for bankruptcy.

In order to pay back funds, firms must prove that they are able to tap the equity and debt markets for funding without using a guarantee from the Federal Deposit Insurance Corp. on new debt issuance. They must also prove to regulators that they are able to continue prudent lending to stimulate the economy, maintain required capital levels and meet funding obligations to counterparties without government assistance.

The banks were also required to undergo a management review that has led to major changes at the country's largest bank,

Bank of America.

It is unclear which firms will be allowed to redeem TARP investments, though JPMorgan, Goldman Sachs and American Express are widely viewed as approval-ready, and some analysts have suggested that Bank of New York Mellon, Morgan Stanley, State Street are other strong candidates.

The Treasury Department is expected to announce Tuesday that up to nine of the biggest banks have approval to repay their TARP funds, reports say.

Sandler O'Neill Partners analyst Jeff Harte noted earlier Monday the uncertainty due to vague thresholds, which has led to some uncertainty about when or whether major firms will gain the approvals investors crave. For instance,

Wells Fargo has bristled against regulatory scrutiny, and is taking an unusual approach to raise funds. It is generating a wide swath of its capital requirement internally, through earnings and other means, and may butt heads with regulators who have set limitations on that method.

There's also the question of how regulators will handle

TARP-related warrants that provide the government with the right to purchase bank stock.

"While the disclosed criteria formally state the need to successfully access long-term debt and public equity markets, the actual amount of debt and equity that must be raised has not been detailed," notes Harte. "Not surprisingly, the vague criteria afford regulators flexibility in determining whether an individual bank is healthy enough to survive without needing additional government support."