BOSTON — A state agency that oversees health insurance for public employees said Thursday it would reconsider its decision to limit offerings for hundreds of thousands of state workers and retirees, following harsh criticism of the move from labor unions and legislative leaders.

The Group Insurance Commission said it would vote next week to undo a Jan. 18 vote that eliminated three major insurance carriers — Harvard Pilgrim Health Care, Fallon Community Health and Tufts Health Plan — which currently offer coverage plans for an estimated 430,000 state and municipal employees, their dependents and retirees.

Ashley Maagero Lee, chief of staff for the commission, said “candid feedback from members and stakeholders,” prompted the decision to schedule a reconsideration vote.

Unions that represent public workers had angrily denounced the previous vote to cut in half the number of insurance carriers available to their members, a move that commission officials estimated would save the state about $20 million.

Labor leaders faulted the commission for rushing to take the vote without enough input from stakeholders and forcing rank-and-file workers to bear the brunt of the state’s efforts to control runaway health care costs.

Peter MacKinnon, president of Local 509 of Service Employees International Union, expressed relief that the commission was preparing to reverse an “incredibly misguided decision.”

In a statement, MacKinnon thanked state officials and Democratic legislators for “opposing a move that was throwing tens of thousands of Massachusetts families into crisis.”

Democratic House Speaker Robert DeLeo announced Wednesday he was forming a special committee, headed by Majority Leader Ronald Mariano, to review the changes, which he called “very disruptive,” and likely to yield “ambiguous savings.” The Senate Ways and Means Committee planned to hold an unusual oversight hearing on the commission’s plan next week.

Democratic Attorney General Maura Healey had also been critical of the changes. Republican Gov. Charlie Baker had faulted the commission for creating confusion with a faulty rollout of the plan, while stopping short of asking that it be scrapped.

If the commission votes Feb. 1 to reconsider, it could then move to accept the full list of insurance carriers that currently offer coverage to public employees.

Under the previous vote, the only remaining options would have been Neighborhood Health Plan of Boston, Health New England of Springfield and UniCare.