In a podcast conversation with British actor Russell Brand on Friday, Governor Ron DeSantis of Florida rejected characterizing the January 6, 2021 attack on the Capitol as a plot organized by supporters of former President Donald J. Trump to disrupt the transfer of power.

“It was not an insurrection,” DeSantis said, continuing to walk a tightrope on the issue of whether the former president, his main rival for the 2024 Republican nomination, is responsible for the riots.

When Brand brought up the likelihood that Trump would soon be impeached for his role in trying to overturn the 2020 election and asked DeSantis if he would pardon Trump, the Florida governor dodged the question. Instead, he accused the media of exploiting the issue.

“These are people who were there to attend a demonstration and then they were there to protest,” he said. “Now it turned, and it turned into a riot. But the idea that this was a plan to somehow overthrow the United States government is not true, and it is something that the media had made up just to try to get the most out of it and use it for partisan and political purposes.”

While Mr. DeSantis called the riot “unfortunate,” he criticized the more serious charges the Justice Department brought against some of those who participated in the attack.

“I know a lot of people who were there who were just there,” he said. “They had no plans to do anything.”

He continued: “But to say that they were seditious is simply wrong.”

This week, Trump publicly acknowledged that he could soon face federal prosecution in connection with the January 6 attack, adding to his legal baggage.

He is already dealing with two indictments, one in June for handling classified documents after leaving office and the other in March in a secret money case in New York.

A grand jury in Georgia is also weighing criminal charges against Trump for his actions after the 2020 election, when he pressured state election officials to “find” votes to overturn his defeat there.

But the confluence of criminal cases does not appear to have hurt Trump’s actions with his Republican base. Lead Mr. DeSantis by about 30 percentage points in national polls.

When Brand brought up Trump’s grip on Republicans, DeSantis, who had narrowed the gap in the polls this year before formally entering the race in May, shrugged off the idea that he was struggling to gain traction.

He said the race was not yet being closely watched by GOP primary voters and that national polls were not an indicator of success in the early nominated states.

As Trump mocked him for the enthusiasm for his candidacy, DeSantis recently expanded his tightly controlled media presence beyond the right-wing friendly outlets. His efforts began with an interview on CNN and included his conversation with the tattooed Mr. Brand, which appeared on YouTube and Rumble, a popular streaming site among conservatives, before moving entirely to Rumble.

Brand, who has leaned to the right and spread conspiracy theories about Covid vaccines, enthused about DeSantis’ response to the pandemic and his political acumen.

“This is a very early season,” DeSantis said. “Most people aren’t paying attention during the summer.”