Cleveland's police union has called for the suspension of a state law allowing people to carry firearms during the Republican National Convention following the killing on Sunday of three police officers in Louisiana.
But Ohio's governor says he's powerless to act.
Donald Trump enters the crucial week trailing Clinton in most national opinion polls and needs a bounce from the convention to vault him into a more competitive position.
He's seized on the shooting deaths in Baton Rouge, Louisiana, to bolster his case that the United States is leaderless and he is the better law and order candidate in the November 8 US presidential election than Hillary Clinton.
After the shootings in Baton Rouge, in which three other police officers were wounded, the head of Cleveland's police union, Steve Loomis, asked Governor John Kasich to suspend state laws allowing people to openly carry firearms, but Kasich says he lacks the authority to do this.
"Ohio governors do not have the power to arbitrarily suspend federal and state constitutional rights or state laws as suggested," he said in a statement.
There are no plans to delay Monday's start of the Cleveland convention, where thousands of Republican delegates are gathering amid a threat of protests both for and against Trump.
Security is extraordinarily tight with downtown streets lined by concrete traffic dividers and tall metal fences, propelled by a new urgency after an attacker drove his truck into a holiday crowd in Nice, France, last week, killing 84 people.
Trump's goal at the convention is to get more American voters to take a fresh look at him and, he hopes, to see him in a more favourable light, after his victory over 16 other Republican candidates in a brutal battle marked by insults and inflammatory rhetoric that left many in the party divided.
The convention will also provide Republican faithful with their first look at his vice presidential running mate, Indiana Governor Mike Pence, who was announced on Saturday after a messy selection process.
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