BOSTON — A state agency that oversees health insurance for public employees has reversed its decision to limit offerings for hundreds of thousands of state workers and retirees, following criticism from labor unions and political leaders.

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

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

Democrats including Attorney General Maura Healey and House Speaker Robert DeLeo criticized the earlier vote.