The crowd cheered. The pork was charred. And then someone shouted at former President Donald J. Trump, asking him to identify his biggest challenger in the 2024 Republican primary.

“Don’t see him,” Mr. Trump replied.

Mr. Trump signaled that he was looking past his leading rival, Ron DeSantis, on Saturday, as the two candidates converged at the Iowa State Fairgrounds. But his campaign team took every opportunity to needle the Florida governor.

Though the two candidates never crossed paths, Mr. Trump’s appearance was scheduled to coincide with Mr. DeSantis’s visit. Mr. Trump engineered a boisterous arrival, which included his private plane buzzing overhead, as Mr. DeSantis finished flipping pork chops. And Mr. Trump brought with him a bevy of Florida House members who had endorsed him over their own governor.

It was a rare moment of side-by-side comparison for Mr. Trump and his main opponent, and the mob of supporters following Mr. Trump’s every move underscored his superior standing. Mr. Trump leads Mr. DeSantis by an average of more than 30 percent nationally, though his margin is slightly smaller in Iowa — a gap that his rivals hope will narrow, as the criminal cases against him proceed. The first contest in 2024 is widely seen as the best opportunity to slow Mr. Trump’s march to the nomination.

Mr. Trump has repeatedly tried to assert his dominance as the front-runner, citing his polling advantage in social media posts and nearly every speech. But the overlapping appearances on Saturday marked just the latest instance of Mr. Trump’s trying to overshadow Mr. DeSantis in Iowa, a sign of how his team views Mr. DeSantis: as his lone serious rival.

The two men cut strikingly different paths at the fairgrounds, as they wound their way through the pens of pigs, past the 600-pound sculpture of a cow carved in butter, and stands selling local delicacies, like deep-fried balls of bacon and cheese.

Mr. DeSantis, joined by his wife, Casey, and their three children, wore jeans and what has become his standard Iowa-casual fare of a custom-made, short sleeve button-down fishing shirt with his name and title emblazoned on his chest. He rode the Ferris wheel, played fair games and crashed bumper cars.

Mr. Trump took to the fairgrounds in a navy suit, with cuff links, and was greeted by a throng of cheering supporters at every stop. He signed hats, waved to the crowds and petted a goat before being driven to the Steer N’ Stein building, where he gave brief remarks.

It is not clear when the two men will be in the same place at the same time. Touting his sizable polling lead, Mr. Trump has said it would be “stupid” for him to attend this month’s first debate of the primary, in which Mr. DeSantis and the rest of his rivals have struggled to gain traction.

But on Saturday, there was plenty of old-school politicking and political theater. At one point, a plane circled the fairgrounds with a “Be likable, Ron!” banner trailing behind. The banner had two inside jabs: The first was a reference to leaked 2018 debate preparations in which Mr. DeSantis was instructed to write the word “likable” in front of him. The second was the exclamation point, which was designed to look like the logo of a previous Florida governor Mr. Trump dispatched in 2016: Jeb Bush.

And before Mr. Trump took the stage, his team handed out leaflets attacking Mr. DeSantis for his position on agricultural issues, calling him an “utter catastrophe” for farmers.

The handouts were a reminder of the asymmetry of the unfolding primary. Day after day, Mr. Trump and his team rip Mr. DeSantis, who has mostly tried to disengage with the former president, lest he anger the sizable portion of the party that likes Mr. Trump but that he still hopes to win over.

Mr. DeSantis and most of Mr. Trump’s rivals have struggled to capitalize on the former president’s three criminal indictments this year, which so far have appeared to rally Republicans to his defense.

Mr. DeSantis has experienced a turbulent few weeks, replacing his campaign manager in recent days as part of the campaign’s third restructuring last month. The shift included bringing in an Iowa expert from his super PAC to a top position, as Mr. DeSantis pledged to visit all 99 of the state’s counties in a series of bus tours. While recording a podcast in downtown Des Moines, Mr. DeSantis predicted on Thursday that he would complete that task by October, a timeline that suggests a particularly aggressive next two months of events in the state.

“You have to earn this nomination, and you have to show up,” Mr. DeSantis said on the “Ruthless” podcast, in a thinly veiled reference to Mr. Trump. “You have to debate. You’ve got to be willing to answer questions.”

Flipping pork chops at a grill station sponsored by the Pork Producer trade association, a traditional stop for presidential aspirants, Mr. DeSantis smiled and chatted with prominent Iowa Republicans, including Senator Joni Ernst, Representative Zach Nunn and Gov. Kim Reynolds.

When Mr. Trump arrived less than an hour later, he packed the area with Florida politicians, who worked the grill as he signed hats and shook hands. A spokesman, Steven Cheung, said that the campaign spent a total of $20,000 buying food and drinks for fairgoers at the pork tent and beer hall.

“We got pork that’s more well done than Ron DeSantis,” said Representative Matt Gaetz, a former DeSantis ally who is backing Mr. Trump and was wearing a “Florida man” shirt.

“I want my president to be the biggest American chest thumper out there,” said Representative Brian Mast of Florida, who came to Iowa to campaign for Mr. Trump. “If you cross him, he will slit your throat, and I get that out of President Trump.”

Everywhere Mr. Trump traveled, he was surrounded by large crowds of cheering supporters angling for selfies and signatures.

As Mr. DeSantis toured the fairgrounds, some people shouted positive encouragement (“We love you, Governor!,” “Go get ’em, Ron!”), to which Mr. DeSantis often responded with a smile or a wave. Others jeered him, some deploying Mr. Trump’s favored nickname of “DeSanctimonious,” which Mr. DeSantis ignored. One woman hurled an expletive at him, as he carried his young daughter on his shoulders.

Mr. DeSantis, a former college baseball player, tried his hand at some fair games, including the milk jug toss. He and his family won at least two giant stuffed Pikachus and what appeared to be a toy koala.

Mr. Trump leads Mr. DeSantis by 24 points among likely Republican caucusgoers, a substantial advantage but one that’s 10 percentage points lower than the commanding position he holds with Republicans nationwide. Every other candidate was in single digits in the recent New York Times/Siena College polls, including Nikki Haley, the former United Nations ambassador who on Saturday sported a shirt that read: “Underestimate me — that’ll be fun.”

The fair can bring surprise encounters for attendees and politicians alike. Former Vice President Mike Pence at one point this week was asked to sign a scavenger hunt list for a fairgoer. (He fulfilled: “Picture of the team with a celebrity.”) Vivek Ramaswamy, the entrepreneur, belted out several verses from Eminem’s “Lose Yourself” after a question-and-answer session with Ms. Reynolds.

Almost every candidate accepted Ms. Reynolds’s invitation to her “fair-side chats” — with the notable exception of Mr. Trump, who has criticized Ms. Reynolds for her plans to stay neutral in the primary and has tried to take credit for her election.

Mr. Trump did not mention Ms. Reynolds in his brief speech at the Steer N’ Stein beer building, which had a “MAGA Meal Day” special that included a double cheeseburger, “freedom fries” and a Coke for $24.

“We don’t want to take any chances,” Mr. Trump told the crowd, saying Iowans were “very special to me.” “We’ll be back,” he said.

Riding the Ferris wheel, high above the fairgrounds, Mr. Ramaswamy peered down to see Mr. Trump waving goodbye to his crowd and ducking into his awaiting vehicle.

Mr. Ramaswamy, who had held his own event at the same spot the night before, wasn’t impressed with the size of Mr. Trump’s audience.

“There he is,” Mr. Ramaswamy said with a straight face. “My crowd was actually — might have been — a little bigger.”

Reid J. Epstein and Nicholas Nehamas contributed reporting from Des Moines.

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