The measure cleared the Republican-controlled chamber 26-7 on Thursday.
Senators stripped a provision from the bill that dealt with concealed weapons agreements between states. The provision would have expanded how the attorney general enters into agreements that allow Ohioans with concealed weapons permits to carry firearms among those states.
Some law enforcement groups opposed the provision because they said it could permit license-holders from states with weaker training requirements to legally carry weapons in Ohio.
The House passed an earlier version of the legislation, and would have to OK the changes before the bill could be sent to the governor.