On a steamy summer morning, Robert F. Kennedy Jr. strode into a hotel conference room in Columbia, South Carolina, amid a barnstorming town hall tour of a state where Joe Biden won close to 49 percent of the vote in the 2020 Democratic primary.

Mr. Kennedy spoke about his 2024 presidential campaign. Democrat pundits say he is a fringe candidate who spreads conspiracy theories. Polls show him with the highest favorability rating of any presidential candidate.

There is no path for Mr. Kennedy to defeat President Biden, critics claim, despite questions about President Joe Biden's age and mental fitness, low approval ratings, and surveys showing that Americans are concerned about the economy.

Earlier this year, the Democratic National Committee voted to give its full support to the president.

Mr. Kennedy agrees that unseating an incumbent president in the same party is a daunting challenge but disagrees with doubters who say he has no chance of securing the nomination.

The 2024 presidential nominee will be announced during the Democratic National Convention in Chicago next summer. Until then, Mr. Kennedy intends to continue to press his case.