BuzzFeed’s newest activist investor, the former Republican presidential candidate Vivek Ramaswamy, wants the company to consider moves like hiring the former Fox News host Tucker Carlson and the N.B.A. commentator Charles Barkley.

Jonah Peretti, BuzzFeed’s founder and chief executive, has already rejected some of Mr. Ramaswamy’s requests out of hand, setting up a clash between the two men.

Mr. Ramaswamy, an investor who has amassed an 8.3 percent stake in BuzzFeed, sent a letter to the company’s board of directors Monday criticizing its business practices and journalistic efforts. Though he has been steadily buying up stock for months, his intentions for the company didn’t become clear until this week.

Before his brief run for president, Mr. Ramaswamy made a fortune in the pharmaceutical business, selling his company’s stake in promising firms to the Japanese conglomerate Sumitomo.

Mr. Ramaswamy is pushing BuzzFeed to add three new members to its board of directors, to hone its focus on audio and video content and to embrace “greater diversity of thought,” according to a copy of his letter shared with The New York Times.

He also recommended that BuzzFeed cut its staff significantly or risk being forced into bankruptcy by its long-term debt obligations.

“Cutting around the edges will not work,” Mr. Ramaswamy wrote. “You require a complete, ground-up re-think of every single piece of content being produced at the company.”

In a reply to Mr. Ramaswamy on Monday, Mr. Peretti said that his letter exhibited “fundamental misunderstandings” about BuzzFeed’s business operations, the values of its audience and the mission of the company. Mr. Peretti owns a special class of voting stock that gives him an effective veto over any drastic remaking of the company or its board.

The two do agree on one thing, Mr. Peretti wrote.

“I’m glad you think BuzzFeed is undervalued — I totally agree!” Mr. Peretti wrote. He said he would schedule a meeting with Mr. Ramaswamy.

Mr. Ramaswamy’s letter comes as BuzzFeed is struggling with the punishing realities of the digital media industry, which have forced the company to take significant action to pay down its debt and preserve its status as a publicly traded company.

BuzzFeed has suffered since it went public in December 2021, reflecting industrywide investor skepticism in digital media companies. The company’s value has plummeted since its Nasdaq debut, falling to $2.80 per share, a drop of 71 percent, as of Tuesday morning.

In recent months, BuzzFeed has taken steps to pay down its outstanding debt, including selling Complex, a pop-culture site known for its coverage of sneaker culture and other streetwear, for $108.6 million. The company still has more than $100 million of debt on its books, according to a recent filing.

Mr. Ramaswamy has some ideas for ways BuzzFeed can jump-start its business. In his letter, the former Republican presidential candidate suggested hiring high-profile “creators” like Mr. Carlson, Mr. Barkley and Aaron Rodgers, the National Football League quarterback. Mr. Carlson and Mr. Rodgers are popular in right-wing media circles for their advocacy of conservative causes.

Elsewhere in his letter, Mr. Ramaswamy criticized BuzzFeed’s 2017 decision to publish a dossier of unverified information that asserted there was a connection between former President Donald J. Trump and Russia; much of that document, the so-called Steele Dossier, was subsequently discredited.

In his reply, Mr. Peretti rejected Mr. Ramaswamy’s request for a mea culpa, saying BuzzFeed was “definitely not going to issue an apology for our Pulitzer Prize-winning journalism,” referring to a 2020 story on the Chinese government’s detention of Muslims.