By the time Republican presidential nominee Donald Trump took the stage at US Bank Arena in Cincinnati, the crowd already had been fed some "raw meat."

That's what Richard K Jones, sheriff of Butler County, Ohio, said he was there to do Thursday night in his warm-up speech to the estimated 21,000 people on hand. They devoured not only his words, but those of former New York City mayor Rudy Guiliani, who delivered the other warmup speech, and finally Trump's.

The rally erupted in cheers when Jones told them not to believe "pundits" who call Trump supporters "deplorable" - a word Democratic nominee Hillary Clinton used to describe his supporters.

But they saved their most raucous reaction for Trump and his message about "this great movement that we've put together. In 26 days, we are going to defeat the corrupt establishment, and we are going to save the United States of America."

It was a big day of electioneering in Ohio as the presidential election enters its final four weeks. While Trump was in Cincinnati, President Barack Obama held a competing rally about 200 kilometres away in Columbus.

The Cincinnati crowd - made up of people dressed in red, white and blue, sporting buttons, baseball caps and even a yarmulke with Trump's "Make America Great Again" slogan - nearly filled the arena.

There were people from the Tea Party group, evangelicals and people who came straight from their jobs as truck drivers and machinists.

"I am just so grateful to have a chance to vote for Donald J Trump for president," said Claudia Schuster, 65, of Sellersburg, Indiana. "You are going to see God give us a miracle on November 8. You are going to see 'we the people' take our country back."

Trump brought the crowd to their feet and set Trump-Pence signs fluttering when he hammered Clinton, the Washington establishment and the media.

The arena at one point erupted in chants of "CNN sucks," showing solidarity with Trump over his claim that the media are to blame for "colluding" with Democrats in the release last week of a recording from 2005 in which he uses explicit terms about women and his aggressive sexual advances.

The media, he said, released the recording because they want to prevent a discussion of the real issues, including the top concerns of conservatives such as gun rights, healthcare and the appointment of Supreme Court justices.

Several people said they support Trump because he is sticking to the issues and they believe he is trustworthy and genuine.

"I think he truly does have a heart for America. That is something that comes through when he speaks," said Mary Harper, 19, of Eastgate, Ohio. "Hillary Clinton has been corrupt for longer than I have been alive."

Ohio is an important state for both candidates, and Trump is trying to build momentum to win it. A new poll released by NBC News shows him 1 percentage point ahead of Clinton, but that is a drop from a poll last week that showed him 4 points ahead.

At the Democrats' rally Obama urged Ohio voters to turn out to help defeat Trump, saying every time he talks he proves himself "unfit and unqualified" to be president.

Obama said Trump was caught on tape saying things that "no decent person would even think, much less say."

In his 47-minute speech Trump tailored his message to Ohioans who have lost manufacturing jobs.

That was a message that resonated with Will Eberle, 45, of Cincinnati, who said he knows people who lost their jobs when factories closed and when Mexican workers arrived, taking manual labour jobs in gardening and construction for lower wages.

"I think he will create more industry over here and not ship jobs out of the country," said Eberle, a machinist.

Trump said Ohio has been one of the hardest-hit states by factory closings and job losses in the steel industry and mining. His economic agenda is three words, he said: "Jobs, jobs, jobs."

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