With just under two months until the Iowa caucuses, former President Donald J. Trump on Saturday returned to the state and made explicit a campaign strategy that he had only hinted at for months.

Speaking in a crowded high school gym, Mr. Trump made clear that he saw a decisive victory in the first Republican nominating contest as the swiftest path to end the Republican primary and focus on a general election race against President Biden.

“You know, we have to send a great signal,” Mr. Trump said. Referring to his Republican rivals, he added, “And then maybe these people say, ‘OK, it’s over now.’”

After his speech concluded, Mr. Trump also made a departure from his normal rally routine. The former president, who has largely eschewed the retail politicking characteristic of the state, stuck around for roughly 10 minutes to pose for pictures and shake voters’ hands.

Mr. Trump’s speech, which covered issues including energy, foreign policy and criminal justice with an Iowa frame, suggested a subtle shift in his campaign’s approach to the Republican primary. For months Mr. Trump has appeared at small “commit to caucus” events, which his campaign hopes will ensure that his popularity in the state propels him to victory in January, pushing out most of the field.

Still, Mr. Trump — who is the front-runner in the Republican primary in both polls and fund-raising — has maintained a fairly light campaign schedule in Iowa.

His challengers, who lag far behind, have barnstormed the state, hoping that a strong showing could weaken Mr. Trump’s foothold and give them a path to the Republican nomination.

On Saturday, Gov. Ron DeSantis of Florida, who has staked his campaign on the state, opened a new Iowa campaign headquarters outside Des Moines. He was joined by Iowa’s popular Republican governor, Kim Reynolds, who recently endorsed him.

Ms. Reynolds, who previously pledged to stay neutral in the caucuses, praised Mr. DeSantis and said that Iowa caucusgoers “expect you to show up, they expect you to earn their votes,” in an apparent dig at Mr. Trump.

But speaking in Fort Dodge, Mr. Trump projected confidence. He relied on a tactic that seemed to reflect his transactional approach to politics: recounting to Iowans what he did for them as president and asking them to return the favor.

At one point, he took credit for keeping their caucuses the first presidential nominating contest, in contrast with Democrats, who shifted Iowa later in their nominating calendar.

“Look, I kept you first in the nation,” he said. “I’m the one that — will you please give me a good show, at least, out of it? OK? Please.”

Mr. Trump reaffirmed his commitment to ethanol, which is important to Iowa’s economy. And as he often does here, he repeatedly touted the $28 billion in aid his administration provided to farmers, money that he has said came from tariffs on China. Mr. Trump suggested that those funds alone should secure him a win in January.

“My guys say: ‘Please, sir, don’t take it for granted that you’re going to win Iowa. It doesn’t sound good,’” Mr. Trump told the crowd. “I say to them, ‘Of course it does. I got them $28 billion. Who the hell else would you vote for?’”

But even as he said Iowans’ support in the caucuses was crucial, Mr. Trump made clear that he was already looking ahead to a general election race against President Biden.

Citing Mr. Biden’s meeting with President Xi Jinping of China, he accused the president of being corrupted by Chinese influence and too soft on the country.

“We have a Manchurian candidate in the Oval Office,” Mr. Trump said, apparently referring to the 1962 film about a Communist sleeper agent in the U.S. government. The reference did not seem to resonate with the crowd.

“You know, ‘The Manchurian Candidate’?” Mr. Trump continued. “Go check it out.”

In another riff on his usual stump speech, Mr. Trump accused Democrats of conducting a witch hunt with their investigations of him, bringing up the so-called Steele dossier, which contained a salacious claim about his encounters with prostitutes in Moscow’s Ritz-Carlton hotel.

Mr. Trump lamented that he had to explain to his wife, Melania, accusations that he instructed the prostitutes to urinate on each other and the bed in the hotel, where President Barack Obama had once slept.

“Actually, that one she didn’t believe, because she said: ‘He’s a germaphobe. He’s not into that, you know?’” Mr. Trump said. “‘He’s not into golden showers,’ as they say they call that.” He shook his head. “I don’t like that idea. No, I didn’t.”

Nicholas Nehamas contributed reporting from Des Moines.