Senate President Robert Stivers said Wednesday that the measure would have provided "much needed stability" to the agencies affected by the measure.
The bill was aimed at providing pension relief for the state's 118 quasi-governmental agencies, including rape crisis centers, public health departments and some universities.
Bevin says he will call lawmakers back for a special session to fix the bill. He said it had provisions that violated the "inviolable contract'' - the language within state law that guarantees recipients get the benefits promised when they were hired.
Stivers says before a special session happens, the governor needs to "set the parameters for what he is willing to sign" into law.
Reaction to the veto was mixed. The advocacy group Kentucky Government Retirees commended Bevin for nixing a bill it said exposed the Kentucky Retirement Systems to "unjustified risk." Kentucky House and Senate Democratic leaders said: "This is not how you govern."
