Robert F. Kennedy Jr. sought to make the case on Sunday that he can do something no third-party or independent candidate has come close to doing in modern U.S. history: win a presidential election. Although polls show him far behind, both major-party campaigns, those of President Biden and former President Donald J. Trump, view Mr. Kennedy as a potential spoiler.

Speaking at a rally on Long Island outside New York City, Mr. Kennedy cited polls that he said his campaign had conducted, showing him winning in two scenarios: one in which he faced only Mr. Biden without Mr. Trump in the race, and one in which he faced Mr. Trump without Mr. Biden.

The reason he is behind in a three-way race, he maintained, is that “so many Americans are voting out of fear.”

“Their only strategy is to try to keep me off the ballot and then to make everybody terrified of Donald Trump,” he said of Democrats, “and on the other side, they do the same thing,” he added of Republicans. “When somebody is telling you to vote out of fear, they are trying to manipulate you into abandoning your values,” he said.