Gov. Ron DeSantis of Florida raced to respond to news that former President Donald J. Trump had been indicted a third time not by opining one way or the other on the new federal charges, but by leveling an unusual attack at residents of the District of Columbia, where the case is being prosecuted.

Suggesting that Mr. Trump could not get a fair trial if the jurors were residents of the nation’s capital, an overwhelmingly Democratic city, Mr. DeSantis called for enacting reforms to let Americans have the right to remove cases from Washington, D.C. to their home districts.

“Washington, D.C. is a ‘swamp’ and it is unfair to have to stand trial before a jury that is reflective of the swamp mentality,” Mr. DeSantis wrote on Twitter. “One of the reasons our country is in decline is the politicization of the rule of law. No more excuses — I will end the weaponization of the federal government.”

The judge assigned to Mr. Trump, who was indicted on charges related to his efforts to overturn the 2020 election, is Tanya S. Chutkan, a D.C. District Court judge who has routinely issued harsh penalties in Jan. 6-related cases against people who stormed the Capitol.

The Republican candidates, who have sought to overtake the former president’s substantial lead in early polls with little success, have campaigned amid a backdrop of Mr. Trump’s legal battles that have sucked up valuable airtime and dominated media coverage. Here’s what the others said on Tuesday:

• Former Vice President Mike Pence, who was present at the Capitol during the Jan. 6 attack and was the target of some rioters — and whom the indictment describes as a key target of Mr. Trump’s pressure campaign to overturn the 2020 election — said that the indictment “serves as an important reminder: Anyone who puts himself over the Constitution should never be President of the United States.”

• Senator Tim Scott of South Carolina, in a statement to The Times, echoed a common refrain among Republicans: that the Justice Department, under the Biden administration, had been weaponized against Mr. Biden’s political opponents. He referenced the case against Hunter Biden, Mr. Biden’s son, and said, “We’re watching Biden’s D.O.J. continue to hunt Republicans while protecting Democrats.”

• Vivek Ramaswamy, a tech entrepreneur and one of Mr. Trump’s most vocal defenders in the 2024 field, called the indictment “un-American.” He sought to absolve Mr. Trump of any responsibility for the Jan. 6 attack on the Capitol and reiterated his previous promise that, if elected, he would pardon Mr. Trump. “The corrupt federal police just won’t stop until they’ve achieved their mission: eliminate Trump,” he said, and added: “Trump isn’t responsible for what happened on Jan 6. The real cause was systematic and pervasive censorship of citizens in the year leading up to it.”

• Former Representative Will Hurd of Texas, who has refused to pledge his support to Mr. Trump if he is the eventual nominee, was the first candidate to respond to the new indictment. “Let me be crystal clear: Trump’s presidential bid is driven by an attempt to stay out of prison and scam his supporters into footing his legal bills,” Mr. Hurd wrote. “His denial of the 2020 election results and actions on Jan. 6 show he’s unfit for office.”

• Former Gov. Asa Hutchinson of Arkansas, who is running an explicitly anti-Trump campaign, reiterated his earlier calls for Mr. Trump to quit his campaign, calling him “morally responsible for the attack on our democracy.” Mr. Hutchinson said that if Mr. Trump does not drop out of the race, “voters must choose a different path.”