In an announcement Monday, attorney Robert F. Kennedy Jr. said he is launching an independent campaign for president, leaving the Democratic Party and embarking on a campaign that could pull votes from President Trump as well as from President Biden.

During an even at Philadelphia, Mr. Kennedy said, “I’m happy to say that the old political alignments are dissolving,” before declaring that he plans to seek the presidency with no party affiliation. There had been some speculation that Mr. Kennedy was courting the Libertarian Party.

“I must first declare my own independence, independence from the Democratic Party and from all other political parties,” Mr. Kennedy said. “I haven’t made this decision lightly. It’s very painful for me to let go.”

At his campaign event, Mr. Kennedy said that would be uniquely positioned to bridge the partisan political divide while railing against the “uniparty.”

Mr. Kennedy also promised that as an independent, he would be able to stand up to “big oil,” “big tech,” military contractors, big banks, “big polluters,” “corporate capture of regulatory agencies,” and the surveillance state. He said he wants a foreign policy that puts “peace and prosperity first.”

“As president, I’m going to work with officials of both parties who want to work with me in serving our nation,” Mr. Kennedy said, adding that “every president enters office promising to unite the nomination,” but that none ever do.

Mr. Kennedy also addressed the question looming over his independent run, whether his candidacy would act more as a spoiler for Mr. Trump or for Mr. Biden.

“They say my impact is only going to draw votes from the other candidates,” Mr. Kennedy said. “The truth is they’re both right. My intention is to spoil it for both of them and only that inside-the-Beltway myopia deludes them into thinking that we have no chance of winning.”

Far away from Philadelphia, Mr. Trump’s campaign is gearing up to attack Mr. Kennedy, who consistently polls more favorably among Republicans than Democrats. This suggests he would likely pull more voters from Mr. Trump.

“We’re gonna be dropping napalm after napalm on his head reminding the public of his very liberal views, dating back to 2012,” a person familiar with Mr. Trump’s campaign’s preparations told Semafor on the issue. “We have a lot of stuff on him.”

The Republican National Committee is also prepping to attack Mr. Kennedy’s campaign, sending out emails Monday with “23 Reasons to Oppose RFK Jr.”

“RFK Jr. knows full well he’ll ‘take more votes’ from the Republican nominee; that’s why he’s running,” the email reads. “But do not be fooled — the only way to reverse America’s decline at the hands of Biden is to elect a Republican as president next year.”

On the Democratic side, Mr. Kennedy’s campaign has not drawn any public acknowledgment from Mr. Biden. Democrats have, though, expressed concerns over potential third-party spoilers in 2024, including Mr. Kennedy.

In addition to Mr. Kennedy’s bid, a professor, Cornel West, is running as an independent. The nonpartisan group No Labels has also said it plans to put up a candidate if Mr. Trump and Mr. Biden are the nominees.

For both Mr. Kennedy and Mr. West, ballot access will be a key issue for their campaigns. The first deadline for a candidate to file for ballot access is October 15. The issue of ballot access could stand in the way of not only third-party candidates but also partisan candidates who might be seeking to make a late entry to the race.

Mr. Kennedy’s announcement drew immediate condemnation from his family, including filmmaker Rory Kennedy, human rights activist Kerry Kennedy, Congressman Joe Kennedy II, and Lieutenant Governor Kathleen Kennedy Townsend of Maryland.

“The decision of our brother Bobby to run as a third party candidate against Joe Biden is dangerous to our country. Bobby might share the same name as our father, but he does not share the same values, vision or judgment,” the siblings wrote. “Today’s announcement is deeply saddening for us.”