A bipartisan Senate bill quickly moving toward passage could allow two of the nation’s biggest banks to reduce the amount of money they must keep on hand as a buffer against collapse by a collective $30 billion, an internal analysis by a top banking regulator has found.

That reduction in capital could weaken one of the safeguards Congress helped put in place after the Great Recession, some banking experts say.

The analysis by the Federal Deposit Insurance Corporation, a government agency that helps oversee the nation’s banking system, found that JPMorgan Chase, which has $2.6 trillion in assets, could lower its required capital stockpile by $21.4 billion, if federal regulators decide the law applies to it. Citigroup, which has $1.9 trillion in assets, could reduce its capital position by $8.6 billion. The analysis was obtained by The Washington Post.

The report comes as the Senate is weighing legislation to scale back banking regulations passed as part of the 2010 Dodd-Frank law, which was forged in response to the 2008 crisis. The bill cleared a procedural Senate hurdle this week with support from all voting Republicans and 17 senators in the Democratic caucus, suggesting the chamber will eventually pass it, probably next week.

Proponents say the bill reduces regulatory burdens for midsize banks that don’t pose a risk to the financial system, but liberal Democrats, the Congressional Budget Office and some banking experts have said it could expose two of the biggest financial firms to new risks. That’s because it contains language that would allow regulators to reduce how much capital some banks are required to hold.

Banking experts widely agree that by holding substantial amount of capital in recent years, banks have been less vulnerable to the type of crisis that nearly toppled the world financial system a decade ago. But there’s disagreement on Capitol Hill and among experts about whether the Senate legislation could free JPMorgan and Citigroup to hold less capital. Defenders of the bill, and even some of its opponents, say JPMorgan and Citigroup would not be subject to lower capital requirements even if the bill passes.

At issue is a special capital surcharge imposed by regulators on banks holding more than $250 billion in assets. For every dollar of assets they have on their balance sheet, these banks are required to keep an offsetting percentage in capital.

The Senate bill would allow banks to not count certain safe assets in that ratio if the bank was determined to be “predominantly engaged” in custodian banking. Three banks — Bank of New York Mellon, State Street and the Northern Trust Corporation — would be mainly affected by this provision.

These banks play a special role in the financial system, where they primarily hold on to assets on behalf of financial institutions and do not engage in either trading activities of their own or provide services to ordinary consumers. Some experts believe that they can be subject to less rigorous rules.

JPMorgan and Citigroup, though they have much broader businesses, also take part in custodial banking activities and, as a result, could also argue that they should benefit from the new rules, as critics of the bill fear.

Ultimately, the decision on how to enforce the new law is expected to fall to the nation’s banking regulators — the Federal Reserve, the Office of the Comptroller of the Currency and the FDIC.

Earlier this week, the Congressional Budget Office gave the two Wall Street giants even-odds of getting regulatory approval to reduce their capital if the legislation passes. Sen. Bob Corker (R-Tenn.) proposed an amendment to the bill on the Senate floor Thursday to make clear that only custodial banks would benefit from the new capital requirements.

The FDIC report was based on the premise that JPMorgan and Citigroup would be allowed to reduce their capital, but the agency was not making any conclusion about whether they would or should be.

“It’s a significant reduction in capital for banks that are highly systemic. Why do we want to do that?” said Sheila Bair, who served as chair of the FDIC under former presidents George W. Bush and Barack Obama. Bair said she thinks it is probable JPMorgan and Citigroup qualify for the exemption. “When you get into a downturn, you need your banks to keep functioning. Highly leveraged banks — banks overburdened with debt themselves — will pull back, and that will make the next recession much, much worse.”

Some experts fear the legislation could be only the beginning of relaxed capital standards for big banks. “It’s a very slippery slope,” Bair said.

Paul Volcker, who served as chair of the Federal Reserve Board for nearly a decade, also told the Senate Banking Committee in a letter that the new capital requirements “would put Congress under pressure to expand the exclusion.”

“If this applies to JPMorgan, it would allow them to fund themselves with a lot fewer resources to handle a crisis by allowing them to take on far more risky debt,” said Mike Konczal, a banking expert at the Roosevelt Institute, a left-of-center think tank. “It would allow them to jack up their profits in the short term but put everyone else at risk because they’d have less resources to handle a crisis in the long run.”

The FDIC analysis shows the required capital surcharge for JPMorgan, currently $159.7 billion, would decline to $138.2 billion, or 13.4 percent, if the bank were granted an exemption. Citigroup, meanwhile, would see its capital surcharge decline from $121.1 billion to $112.5 billion, or 7.1 percent.

As first reported by the Intercept, Citigroup has pushed Congress to broaden the new exemption, suggesting to the bill’s proponents that they will not benefit from it as currently drafted. “As Congress has sought to make a common sense change to the way capital rules treat custody assets, we have asked that they apply that change to all custody banks to maintain a level playing field in this important business,” a spokesman for Citigroup said.

A JPMorgan spokesman did not return a request for comment.

Defenders of the proposal have adamantly denied that either JPMorgan or Citigroup would benefit from the measure.

Sen. Mark R. Warner (D-Va.), who backs the bill and was one of the main architects of the 2010 overhaul of banking rules, said it was part of CBO’s job to raise “hypothetical red flags” and said the intention of the bill was not to benefit JPMorgan and Citi.

“The legislation makes clear that the [holdings requirement change] will be granted only to custody banks, which is because of their unique business model,” a Warner spokeswoman said in an email.

“I think the CBO is not exactly the source of analysis on risk,” added Sen. Heidi Heitkamp (D-N.D.), a co-sponsor of the bill, in an interview. “A lot of this is being exaggerated to make the case against this bill.”

Citigroup was the top recipient of federal bailout money during the 2008 crisis, ultimately claiming $476 billion in aid, according to the inspector general for the bailout. The money was eventually paid back. JPMorgan was on stronger footing during the crisis but was still aided in buying Bear Stearns and accessing a number of other emergency programs launched by the Federal Reserve and Treasury.

Renae Merle and Erica Werner contributed to this report.