Big banks have been pressing US regulators to reconsider a controversial rule requiring them to hold greater buffers against future losses, and this week they got what they wanted.

Federal Reserve Chair Jay Powell and FDIC Chair Martin Gruenberg both said Thursday they anticipate changes to the rule following pushback from lenders, community groups, Republicans, and even some Democrats.

Powell told Senate lawmakers that "I expect there will be material and broad changes," and "we won’t hesitate" to re-propose the rule if that makes sense — repeating a point he made to House lawmakers Wednesday.

Gruenberg told reporters separately "I certainly think we anticipate making changes in the final rule based on the extensive comments that we've received."

The concerns about the capital rule — the most aggressive change to how banks are regulated since the aftermath of the 2008 financial crisis — range from harm it could do to the US economy to ways in which it would reduce access to mortgages for disadvantaged home buyers.

The willingness of regulators to change what they already proposed highlights the increased sway that big banks have in Washington, a sharp contrast to the harsh political scrutiny they received in the aftermath of the 2008 financial crisis.

"We also see this as potentially marking an important inflection point whereby the regulatory burden levied on the largest banks" after the 2008 crisis "could be nearing a peak," Ebrahim Poonawala, a bank analyst for Bank of America, said in a note this week.

Senator Elizabeth Warren (D-Mass.) on Thursday accused Powell of flip-flopping on tougher capital rules after pledging last year to be more aggressive with supervision following the failures of several mid-sized lenders such as Silicon Valley Bank.

"You have gone weak-kneed on this," she told Powell during a Senate Banking Committee hearing.

Powell said the capital rule — known as Basel III — is not directly related to what happened to Silicon Valley Bank and that the Fed is taking other steps to heighten supervision of specific banks.

“You will see I am doing exactly what I said I would do,” Powell said.

At issue are higher capital requirements that were unveiled last summer by Fed Vice Chair for Supervision Michael Barr. Those requirements focused on the amount of capital that banks must have in reserve to protect themselves from insolvency.

Regulators have said the proposal would result in a 16% increase in capital levels and a 20% increase in risk-weighted assets for big banks.

In the months since, the banks have launched a campaign to roll back the new rules — or scrap them entirely. Many banks submitted letters to the Fed listing the many problems they have with the rules ahead of a deadline for those comments that ended Tuesday.

The banks have contemplated suing if the rules don’t get changed. JPMorgan Chase (JPM) CFO Jeremy Barnum openly discussed that possibility with reporters in January.

Suing the bank’s own regulator "is never a preferred option," he said, but "it can’t be taken off the table."

The Bank Policy Institute, a trade group representing JPMorgan and other big banks, has reportedly hired a lawyer to prepare a lawsuit if the rules don’t get changed, according to a report by Semafor.

One big bank lobbyist, Financial Services Forum president and CEO Kevin Fromer, said he was "encouraged" by Powell’s assurances this week.

"We agree: Broad and material changes are needed to the proposal to avoid significant harm to the economy, businesses of every size, and American households," he said.

"To achieve that, we continue to believe that a re-proposal is the best approach to giving the public a well-justified and data-based rule that is consistent with the plans of other jurisdictions."

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