State Sen. Peggy Lehner, of Kettering, was among Republicans who voted to let Kasich's veto stand.
"We have a gun problem in this country and we need to recognize that," she said.
Dayton Mayor Nan Whaley took to her Facebook page to criticize the action from lawmakers.
“The General Assembly overrode Governor Kasich’s veto of House Bill 228, stripping local governments of the ability to create and enforce reasonable restrictions on firearms in our cities,” Whaley said. “Keeping our cities safe is among our most important duties as local elected officials, and this action by the General Assembly undermines our ability to make local decisions about our communities' safety.”
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Earlier coverage:Ten months after reversing his position on gun control, Ohio Gov. John Kasich on Wednesday vetoed a gun rights bill that would have shifted the burden of proof in self-defense shooting cases from the defendant to the prosecutor.
Kasich rejected House Bill 228, even though the more controversial elements — the so-called ‘Stand Your Ground’ provisions — were stripped out before the legislation was sent to the governor.
The Ohio General Assembly returns to Columbus after Christmas for final votes before the end of the two-year legislative session. If lawmakers want to override Kasich’s veto, they’ll need to muster 60 votes in the House and 20 in the Senate. Many lawmakers are expected to be out of town for the holidays.
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The Associated Press contributed to this report.