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Gov. John Kasich of Ohio released a statement expressing grief at the attack in Baton Rouge, La., but a spokeswoman said he would not move to restrict the brandishing of guns around the Republican National Convention in Cleveland, which begins on Monday.

Emmalee Kalmbach, a spokeswoman for the governor, said in an email that Mr. Kasich did not have the power to block people from carrying legal firearms in the general vicinity of the convention.

On Sunday afternoon, Stephen Loomis, the president of the Cleveland Police Patrolmen’s Association, said that Mr. Kasich should temporarily suspend “open carry” for the sake of security. Mr. Loomis said in an interview with CNN that he did not care “if it’s constitutional or not.”

Mr. Kasich’s office rejected the idea as legally impossible.

“Ohio governors do not have the power to arbitrarily suspend federal and state constitutional rights or state laws as suggested,” Ms. Kalmbach said. “The bonds between our communities and police must be reset and rebuilt – as we’re doing in Ohio – so our communities and officers can both be safe. Everyone has an important role to play in that renewal.”

The Secret Service has tighter restrictions for people attending the convention inside the Quicken Loans Arena, including a ban on firearms.