Republican presidential hopeful businessman Donald Trump finishes a rally on July 25, 2015 in Oskaloosa, Iowa.
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OSKALOOSA, Iowa—Donald Trump said there was no cap in the amount of money he would be willing to put into his campaign for the Republican nomination for president if his message continues to resonate with voters.

Speaking at a free-wheeling press conference following a rally in this city east of Des Moines, Mr. Trump also attacked Republican rivals Jeb Bush and Scott Walker and Democrat Hillary Clinton with accusations that they were beholden to wealthy donors.

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Mr. Trump, a real-estate developer and television personality, has almost entirely self-financed his campaign so far.

“Bush is controlled by those people. Walker is controlled by those people. Hillary Clinton is controlled by those people. Trump has none of those people,” he said Saturday afternoon. “I’m not controlled. I do what’s right for the people.”

Mr. Trump was particularly pointed in his attacks of Mr. Walker. He criticized the Wisconsin governor’s handling of his state’s economy and accused him of flip-flopping his stance on the Common Core education standards.

While once friendly with the governor, Mr. Trump said he felt free to criticize Mr. Walker after a fundraising invitation sent by one of his donors called Mr. Trump a “DumbDumb.”

“I said ‘hey now, the gloves are off,’” said Mr. Trump, who called the fundraiser a “stupid person.”

A spokeswoman for Mr. Walker’s campaign didn’t immediately respond to a request for comment.

Mr. Trump spoke before more than 1,000 people who gathered for a “family picnic” and speech that his campaign sponsored. Attendees filled the auditorium of the city’s high school and spilled into a space in the neighboring middle school, with 1,300 people registering to attend, a campaign official said.

The rally was originally scheduled to be held at a city park in Oskaloosa last month, but was rescheduled for a larger facility, Mr. Trump’s state director said.

The largely white crowd ate hamburgers cooked on long grills and salads served in silver chafing dishes.

“He’s saying the things we really feel,” said Gary Staggs, a 55-year-old small business owner from Oskaloosa.  “Politicians can’t say them because they are so afraid of somebody they will offend.”

Mr. Trump delivered a nearly hourly long monologue without notes that touched on the imbalance of trade with China, his wealth and Iowa’s hot weather.

“I love you people. I love Iowa. But it’s hot as hell and I’m sweating like a dog,” said Mr. Trump, who wore a full suit.

Mr. Trump stuck to his criticisms of Mexico and illegal immigration to the U.S. from his country. He called for a system of immigration based on merit, but didn’t discuss specifics of his plan when asked about it after the speech.

After being criticized by veterans groups for attacking Arizona Sen. John McCain’s war record, Mr. Trump brought on stage a stack of papers he claimed to have been sent to him from former military men who supported him. Audience members waved printed signs stating “Veteran for Trump.”

Mr. Trump has lobbed colorful attacks at rivals since declaring he was running for president last month. He said he would tone down his criticisms if he was elected president, and singled out Texas Sen. Ted Cruz and neurosurgeon Ben Carson for maintaining a civil tone towards him.

Mr. Trump declined to discuss specific in response to a wide-range of questions posed to him by reporters. He would not say if he was preparing for the debates or if he was taking pointers from policy advisers. He couldn’t say who would make up a Trump cabinet.

Asked if he would join some Republicans’ calls to cut Social Security benefits, Mr. Trump said it wasn’t necessary because he would bring so much economic activity back to the U.S.

Flanked by a large security detail in suits, Mr. Trump stood with well-wishers who snapped photos with him as he left. He posed before a “Trump” campaign bus, but then got into a black SUV to leave Iowa by plane.