The Senate is expected to soon take up a separate House resolution rolling back that state rule.

The consequences of the Senate’s votes could be significant. The Labor Department rules were designed to give around 13 million people in the five states access to retirement accounts, out of 55 million nationwide who lack employer-sanctioned retirement programs. Among those affected most by the measure passed on Thursday will be small business owners and employees who have blanched at the cost of conventional 401(k) plans or pensions.

In a joint statement, Mayor Bill de Blasio of New York, the City Council president, the city’s public advocate and a council member said that they were “deeply disappointed that Congress has voted to overturn the Department of Labor rule providing a safe harbor for us to create retirement savings plans for private sector employees.”

“This vote does little more than block them — the majority of whom are women and people of color — from securing their futures,” the statement said.

Thursday’s vote was only the latest regulation that Republicans have rolled back this year using the 1996 Congressional Review Act, which had hardly been used in the two decades before Mr. Trump’s inauguration. Seven rollbacks have been signed into law by President Trump, with several others awaiting his signature.

But in this case, Republicans were replacing local regulatory authority with federal control — taking up a cause of investment banks that fear competition from state and local governments. The Obama Labor Department’s rule actually gave states more autonomy in reaching contracts with private-sector financial managers to handle the savings accounts. State governments could be administrative conduits, keeping records while passing on funding to private consultants, who would manage the money in place of state treasurers.