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PELLA, Iowa — Donald J. Trump’s reaction to the potential run of Michael R. Bloomberg in the presidential race was simple: Bring it on.

“I would love to see Michael run — I would love the competition,” Mr. Trump said in a brief interview before a rally of several hundred people who lined up for hours to see him here.

He was responding to a New York Times report that Mr. Bloomberg had asked his advisers to draw up plans for a potential run as an independent candidate under specific circumstances, particularly if Senator Bernie Sanders wins the Democratic primary and the Republicans choose Mr. Trump or Senator Ted Cruz.

“I’d love to see what would happen,” Mr. Trump said. Asked to compare his own business acumen to Mr. Bloomberg’s, Mr. Trump said, “It’s different kinds of business, it’s a very different kind of business, but I would say that if he ran, I’d be very happy about it.”

He described Mr. Bloomberg, the former mayor of New York, as a friend, and said he “called me to help him out” with a construction situation in the Bronx, at what is now a Trump golf course on a former city landfill at Ferry Point.

Mr. Trump repeatedly declined the chance to criticize Mr. Bloomberg, although he did say, “He’s the opposite of me in many ways — opposite on guns, opposite on numerous issues.”

But the real-estate developer said Bloomberg Politics, a website and offshoot of Mr. Bloomberg’s media company, “extremely inaccurately and extremely unfairly” covered him. (Mr. Trump, who often describes media coverage as unfair to him, said he was not referring to the two lead reporters there, John Heilemann and Mark Halperin.)

“I have been treated worse by Bloomberg than I think any other group,” Mr. Trump said of the website. “Because of that, I think he’s running.”

Elected in 2001 to City Hall after the Sept. 11 terrorist attacks, Mr. Bloomberg often faced aggressive, at times blistering coverage from the famously gritty New York tabloids. But he has never faced an opponent like Mr. Trump, who has used his media megaphone to dent a range of candidates, including Jeb Bush, Dr. Ben Carson, Senator Ted Cruz and Hillary Clinton.

Last week, Mr. Trump told ABC News that he believed that Mr. Bloomberg would draw votes from Mrs. Clinton if she were the Democratic nominee.