(Updates with Trump comment, Republican briefing comments)
By Steve Holland and Ginger Gibson
CLEVELAND, July 17 (Reuters) - Cleveland's police union called for the suspension of a state law allowing people to carry firearms during the Republican National Convention but Ohio's governor said he was powerless to act despite heightened security concerns with the killing on Sunday of three police officers in Louisiana.
Republican Donald Trump seized on the shooting deaths in Baton Rouge, Louisiana, to bolster his case the United States is leaderless and he is the better candidate in the Nov. 8 U.S. presidential election to restore law and order than his rival, Democrat Hillary Clinton.
It was not immediately clear there was a link between Sunday's shootings and recent unrest countrywide over police killings of black men, one of them a shooting in Baton Rouge about two weeks ago.
Despite a lack of clarity about the motive and specifics of Sunday's incident, Trump said President Barack Obama "doesn't have a clue" on how to handle the problem after Obama voiced concern about inflammatory rhetoric on the campaign trail.
"Our country is a divided crime scene, and it will only get worse!" Trump said.
He issued statements on Twitter on Sunday, a day before the start of the four-day Republican Convention in Cleveland this week due to formally nominate him for the White House.
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 said he lacked the authority to do so.
Kasich, a Republican who lost his bid for the White House to Trump, issued a statement through his spokeswoman Emmalee Kalmbach, saying:
"Ohio governors do not have the power to arbitrarily suspend federal and state constitutional rights or state laws as suggested. 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."
Clinton called the shootings "devastating" and urged the country to work together. "We must not turn our backs on each other. We must not be indifferent to each other," Clinton said in a statement. "We must all stand together to reject violence and strengthen our communities."
OBAMA: SHUN INFLAMMATORY RHETORIC
Speaking at the White House, Obama said that with this week's Republican convention followed next week by the Democratic convention in Philadelphia, political rhetoric would likely be more overheated than usual.
"We don't need inflammatory rhetoric, we don't need careless accusations thrown around to score political points or to advance an agenda. We need to temper our words and open our hearts, all of us," Obama told reporters.
There were 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, 70, a businessman-turned-candidate.
Security was 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.
Jeff Larson, chief executive officer of the convention, said he was not worried about the open carry law.
"There's going to be plenty of law enforcement in downtown Cleveland," he told reporters. "I feel good about the security and what we've done."
Trump sought to link the violence to the U.S.-led fight against Islamic State, writing: "We are TRYING to fight ISIS, and now our own people are killing our police. Our country is divided and out of control. The world is watching."
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.
Republican strategist Hogan Gidley said the violence gave relevance to Trump's message.
"It's something that Donald Trump and his crowd were already prepared to talk about," he said. "This is an epidemic in this country now and we've got to solve it."
NIXON IN 1968
Democratic strategist David Axelrod tweeted that Trump's effort to make himself a law-and-order candidate reminded him of a similar attempt by Richard Nixon in 1968, when the Republican won his first presidential election.
"Someone's been studying '68," Axelrod tweeted.
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 favorable 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.
To that end, many speakers will talk about their views on Trump, from daughter Ivanka to women's pro golfer Natalie Gulbis.
"It's going to be a very personal convention. I mean, you're going to have his family speaking. You're going to have friends who have known him speaking," Trump campaign manager Paul Manafort told CBS's "Face the Nation."
Many longtime party fixtures are staying away.
Republican National Committee Chairman Reince Priebus, who has been a private counselor to Trump, said the convention would help Trump pivot to the general election.
"He's never run for anything before. ... I think it's just taken longer to pivot, and I think he's pivoting," Priebus told NBC's "Meet the Press."
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.
Hoping to win over more traditional Republicans, Trump picked the social conservative Pence over two other finalists, former House of Representatives Speaker Newt Gingrich and New Jersey Governor Chris Christie.
The disorganized nature of the running mate rollout - in which Trump failed to fully project the power of the partnership - had some Republicans worried that they could see more of the same at Cleveland.
(Additional reporting by Kim Palmer and Scott Malone in Cleveland and Timothy Gardner in Washington; Editing by Howard Goller)