PITTSBURGH — Gov. Ron DeSantis of Florida, widely seen as the Republican who poses the biggest threat to Donald J. Trump if they both run for president in 2024, is set to visit Pennsylvania and Ohio on Friday during a national tour with hard-right candidates that appears to be intended to elevate his standing and earn political capital with potential future leaders in battleground states.

As he aims to wrest control of the conservative movement, Mr. DeSantis is appearing with some of its highest-profile and most incendiary figures — midterm candidates who, unlike him, have relentlessly pushed the fiction that the 2020 election was stolen. His rallies on Friday for Doug Mastriano, the Republican nominee for governor of Pennsylvania, and J.D. Vance, the party’s choice for Senate in Ohio, come five days after an event for Kari Lake, the G.O.P. pick for governor of Arizona, and Blake Masters, the nominee for Senate there.

The catch: All of these candidates identify with Mr. Trump’s “Make America Great Again” movement and have his endorsement.

That leaves Mr. DeSantis walking a fine line as he tries to build alliances with Mr. Trump’s chosen 2022 candidates while simultaneously conveying the message that the Republican Party does not belong only to the former president.

Mr. DeSantis and his allies may see a political opening in Mr. Trump’s mounting legal problems. But at the same time, the former president is widely expected to embark on a third run for the White House, and the investigations surrounding him have prompted Republicans to circle wagons around their embattled leader, reaffirming his power over the party.

Supporters of Mr. DeSantis believe he can appeal to many Republicans as a figure who fights the same cultural battles as Mr. Trump but without the chaos and with the ability to win over some moderate voters beyond the party’s base.

A New York Times/Siena College poll last month found that Mr. DeSantis was the clear second choice among Republican voters, with Mr. Trump garnering 49 percent support in a hypothetical 2024 presidential primary and the Florida governor earning 25 percent. No other Republican was in double digits.

On Tuesday, Florida Democrats will decide whether to nominate Representative Charlie Crist or Nikki Fried, the state’s agriculture commissioner, to challenge Mr. DeSantis in November. Mr. DeSantis’s national profile has allowed him to raise more than $130 million in campaign cash, making him a formidable incumbent.

On Friday, Mr. DeSantis, who did not immediately respond to a request for comment, will appear in Pittsburgh with Mr. Mastriano and then speak at an event outside Youngstown, Ohio, with Mr. Vance. On Sunday, he campaigned in Arizona with Ms. Lake and Mr. Masters, as well as in New Mexico with Mark Ronchetti, the Republican nominee for governor, and Representative Yvette Herrell.

In Arizona, Mr. DeSantis highlighted legislation he has signed in Florida, took jabs at President Biden and Democratic leaders in Congress, and attacked the F.B.I.’s recent search of Mr. Trump’s home in Florida — though, as in his other recent remarks, he was careful to criticize investigators rather than defend the former president’s actions.

“They’re enforcing the law based on who they like and who they don’t like,” he said. “That is not a republic. Well, maybe it’s a banana republic when that happens.”

His appearances have been organized by Turning Point Action, a conservative youth group led by Charlie Kirk, 28, who is close to the Trump family and has been a leading purveyor of misinformation about topics including the coronavirus pandemic, the 2020 election and climate change.

Mr. Mastriano’s Democratic opponent, Josh Shapiro, began airing ads this week invoking the man accused of killing 11 worshipers at the Tree of Life synagogue in Pittsburgh in 2018, after posting antisemitic vitriol on Gab. Mr. Mastriano distanced himself from Gab last month, saying he rejected “antisemitism in any form.”

Jewish Democratic leaders in Florida criticized Mr. DeSantis’s planned appearance with Mr. Mastriano in the same city as the Tree of Life synagogue.

“When Ron DeSantis goes to Pennsylvania to campaign for Mastriano, what he’s doing is he’s encouraging all of the bigotry,” said Rabbi Mark Winer, the president of the Florida Democratic Party Jewish Caucus. “He fertilizes the soil in which those seeds of ugliness in America’s soul germinate and come to full blossom.”

Mr. Mastriano, for his part, said that his goal was to “make Pennsylvania the Florida of the North,” adding that Mr. DeSantis had “set the gold standard for the good a governor can do leading a state.”

In Ohio, the DeSantis rally is in the congressional district of Representative Tim Ryan, the Democratic nominee for Senate, whose emphasis on his independence from Mr. Biden and on his support for blue-collar voters is giving Mr. Vance an unexpectedly close challenge in a state that has tilted reliably red in recent years.

Republicans’ worries about the race were confirmed on Thursday when a super PAC tied to Senator Mitch McConnell, the minority leader, said it was reserving $28 million in TV and radio ads to help Mr. Vance, an enormous increase over earlier Republican commitments to the contest.

In Florida, Mr. DeSantis has governed the state as a laboratory for right-wing policy, acting more and more like someone vying for the Republican presidential nomination in 2024 than like the leader of a red-tinged but still fairly evenly divided battleground. While he campaigns to the Trump-loving G.O.P. base as a pugilist fighting “woke” liberals, he has been careful so far in televised ads for his re-election campaign this fall to strike a somewhat different tone.

Most of his ads do not include a message from Mr. DeSantis himself; rather, they feature people praising his handling of the coronavirus pandemic and voice-over readings of thank-you letters his office has received from happy constituents. That message appears geared at holding on to support from independents who are crucial to winning Florida’s still-close statewide elections.

Mr. DeSantis has avoided repeating false claims about fraud in the 2020 presidential contest, preferring to focus on the election laws he has pushed in Florida, including the creation of an office of election crimes and security. On Thursday, he announced that 17 people had been charged with casting illegal ballots in 2020 — an election in which 11.1 million Floridians voted.

At a news conference in June, Mr. DeSantis dismissed a question about whether the 2020 election was rigged.

“I’ve been asked that a hundred different times,” he said. “Anyone have a question on the topic of the day?”

He went on to criticize the Jan. 6 hearings, though he condemned the riot shortly after it happened in 2021.

Some of Mr. DeSantis’s cultural offensives have met legal resistance: On Thursday, a federal judge blocked a key part of one of the governor’s signature laws, known as the Stop WOKE Act, which bans discussions of race that make people uncomfortable in schools and corporations.

“DeSantis has just gone from being awesome to being unbelievably good,” Mr. Jones said, calling him “way better” than Mr. Trump.

Trip Gabriel reported from Pittsburgh, and Patricia Mazzei from Miami.