Federal regulators are considering forcing larger U.S. banks to bear a bigger portion of the cost of cleaning up the banking crisis, a source familiar with the plan said on Monday.

The potential Federal Deposit Insurance Corp plan would charge banks for their share of the cleanup based on their assets rather than their domestic deposits.

Bigger banks, which typically rely less on deposits to fund their balance sheets than smaller banks, would likely have to pay more if the proposal goes through.

The FDIC said in February that it plans to charge the industry a special one-time fee, called an emergency assessment, in the third quarter to help replenish its dwindling fund used to back insured deposits when a bank fails.

It originally proposed charging banks a fee equal to 0.2 percentage points of their deposits, but now is looking at charging banks 0.05 or 0.06 percentage points of their assets, excluding capital, the source said, speaking anonymously because the agency talks are private.

I appreciate the move tremendously, but the reality is it doesn't give us a break, as much as it more equitably charges the larger organizations, said Kevin Kutcher, Chief Executive of Liberty Bell Bank in Cherry Hill, New Jersey, which has about $160 million of assets and four branches in New Jersey.

The assessment will be the subject of an FDIC board meeting on Friday. The FDIC declined to comment.

Banks have continually complained to regulators that the emergency assessment would hit their bottom line at a time they can least afford it.

Barney Frank, the chairman of the House Financial Services Committee, said changing the emergency fee to make it based on assets would appropriately shift the fee burden to larger banks, which rely more on risky assets for funding instead of insured deposits.

Community banks have been unfairly maligned in the public discussion, Frank told Reuters. It's very appropriate to do a more risk-based assessment.

As originally proposed, the fee would have pulled $15 billion from the bank industry to refill the FDIC's deposit insurance fund. The fund took a big hit during the fourth quarter, plunging almost 50 percent to $18.9 billion in preparation for actual and expected bank failures.

The FDIC has said it would reduce the emergency assessment if Congress approved legislation that would triple its borrowing authority with the U.S. Treasury Department to $100 billion. The agency is hoping that will happen in the coming days.

The special assessment would be the first since 1996, when regulators took similar action in the aftermath of the savings and loan crisis.

The shift to fees based on assets instead of deposits comes as the FDIC is also seeking the power to charge bank holding companies, instead of just insured depository banks.

Arthur Murton, the FDIC director of insurance and research, told a Senate subcommittee in March that the agency is currently hindered in its ability to target its fees toward the biggest institutions, such as bank holding companies supervised by other federal regulators.

The FDIC realizes that these assessments are a significant expense, particularly during a financial crisis and recession when bank earnings are under pressure, Murton told lawmakers.

(Reporting by Karey Wutkowski with additional reporting by Dan Wilchins in New York; Editing by Gerald E. McCormick, Steve Orlofsky and Tim Dobbyn)