The elaborate rollout of a Kennedy family endorsement of President Biden on Thursday — talk-show interviews, a campaign event with the president, door-knocking by Kennedys across Philadelphia — was the most powerful sign yet of rising concern in the Biden camp that Robert F. Kennedy Jr.’s independent White House bid presents a serious threat to the president’s re-election prospects.

Members of this prominent Democratic family, including most of Mr. Kennedy’s siblings, had already signaled their support for Mr. Biden. Mr. Kennedy’s estrangement from much of his family had grown increasingly apparent over the years, as he became a leading spokesman against Covid vaccines and promoted conspiratorial theories about the 1968 assassination of his father, Robert F. Kennedy.

But this was the first time Mr. Biden’s campaign had been so aggressively involved in promoting the Kennedys’ strong backing of the president, making an open push to discredit any enduring Democratic credentials Robert F. Kennedy Jr. carries because of his family name.

After leaving the work to outside liberal groups, the Biden campaign has now joined the effort to define Mr. Kennedy beyond the gauzy memory of his father and two uncles, who for many members of Mr. Biden’s fraying coalition, including Black voters, Latinos and blue-collar workers, continue to symbolize Democratic politics in America.

Democratic worries about Mr. Kennedy have grown as he has turned up his attacks on the president and worked to win ballot lines in critical battleground states. Michigan election officials announced on Thursday that he had secured a spot as a member of a little-known third party.