“For years, armies of bank lobbyists & executives have groaned about how financial rules are hurting them,” Ms. Warren wrote on Twitter ahead of the House vote. “But there’s a big problem with their story — banks are making record profits. Congress has done enough favors for big banks — the House should reject the #BankLobbyistAct.”

Ms. Pelosi and Representative Maxine Waters of California, the ranking Democrat on the House Financial Services Committee, wrote a letter to their House colleagues urging them not to support the bill. “We must not allow the G.O.P. Congress to drag us back to the same lack of oversight that ignited the Great Recession,” they wrote.

The overtures did not prevent several Democrats from crossing party lines in favor of the legislation — 33 Democrats voted for it, and one Republican, Walter B. Jones of North Carolina, voted against it.

Democrats have pointed to record profits on Wall Street, saying banks do not need relief from rules given how flush they are with cash. A report from the Federal Deposit Insurance Corporation on Tuesday said that the combined net income of the nation’s commercial banks and savings institutions reached $56 billion in the first quarter of 2018, a 27.5 percent increase from a year ago.

Once the bill is signed by Mr. Trump, small and medium-sized banks will no longer be required to undergo “stress tests” aimed at measuring their ability to withstand a severe economic downturn. The legislation also offers a reprieve to big — but not behemoth — banks, allowing large institutions like American Express and BB & T to no longer be deemed “systemically important” and subject to stricter oversight.

The bill also exempts some loan originators, including small lenders, from certain disclosure requirements under the Home Mortgage Disclosure Act. Democrats say this will open the door to discriminatory practices because the rules required collection of credit scores, loan amounts and interest rates in an effort to expose redlining and lending discrimination.

While the legislation does little to help the very largest banks like JPMorgan Chase, Goldman Sachs and Citigroup, the Trump administration has been working behind the scenes through its regulatory agencies to weaken capital requirements and ease other restrictions on such firms.