Attorney General Mike DeWine also said he would support allowing a trained school official access to a gun during the school day if he were a school board member, but said such decisions should be up to each district.
Statistics show school shooters do most of their damage in the first minute or two of entering a school, so it's unrealistic to think a traditional first responder will be there in time, DeWine said.
"We cannot unless we barricade every school in this country assure that there's never going to be a problem," DeWine said. "But what we can do, and what it's our moral obligation to do as citizens, as elected officials, is to minimize the risk, increase our odds of kids surviving and decrease the odds of something happening."
DeWine said the majority of school safety plans do not meet new guidelines published by his safety task force for such plans, and he will be working with districts to improve those.
Under the plan announced Wednesday, the state police training academy will train educators around Ohio to deal with a shooter. DeWine is also expanding his school safety task force to include mental health officials.
"It is not just a question of what you do when you have an active shooter," DeWine said. "It is how you stop an active shooter from being there. It's how you identify an active shooter."
Parents and guardians have to believe their children are safe at school, said Michael Sawyers, acting state schools superintendent.
"Productive learning environments cannot occur in our state without having safe learning environments for school," he said.
The announcement follows last week's Connecticut massacre in which a gunman shot his mother at home, then entered Sandy Hook Elementary School where he fatally shot 20 students and six adults before taking his life.
DeWine said the announcement was also a follow-up to school safety issues raised by last February's shooting in Chardon that killed three students.
The teen suspect, T.J. Lane, goes on trial next month. Investigators have said Lane, who filed an insanity plea, admitted shooting at students but couldn't say why.