Robert F. Kennedy Jr.’s troubled presidential campaign said Wednesday that it would address its “path forward” at an event this week, even as the candidate himself was in a Long Island court fending off an attempt backed by the Democratic Party to block him from New York’s ballot for a second time.

The event will be held in Phoenix on Friday, the same day that former President Donald J. Trump is expected to campaign in nearby Glendale, Ariz. On Tuesday, Mr. Kennedy’s running mate, Nicole Shanahan, said that the ticket was considering endorsing Mr. Trump; hours later, Mr. Trump said he would welcome it.

Mr. Kennedy, returning to court in Mineola, N.Y., after a lunch break, did not respond to questions about whether he would drop out of the race.

Mr. Kennedy began running for president last year as a Democrat, challenging President Biden. He later embarked instead on an independent campaign that unnerved both major parties, which feared he would siphon critical support from their candidates.

In recent weeks, as his campaign’s money ran low, Mr. Kennedy’s support in national polls, once in the low double digits, plunged to about 5 percent. It was nowhere near sufficient to have a shot at victory, but still enough to potentially affect the results of the election, depending on his numbers in key swing states.

While the Democratic Party had dedicated substantial resources to contesting his candidacy, including legal challenges to his ballot access effort, recent polls suggested that Mr. Kennedy was drawing votes primarily from Mr. Trump, and that his presence in the race helped Vice President Kamala Harris.