The magazine’s owner, Chris Hughes, who was a founder of Facebook, had recently hired a new chief executive, Guy Vidra, against the wishes of Mr. Foer. The appointment caused a clash between the more literary tradition of The New Republic and the Silicon Valley business approach advocated by Mr. Vidra, who had come from Yahoo. Mr. Vidra said in a memo to the staff on Thursday that he wanted to reimagine the publication “as a vertically integrated digital media company.”

In an interview on Friday, Mr. Hughes seemed hurt by the idea that his staff had turned against him, and he cited the need to adjust operations to try to make the magazine more profitable. “The reality is that Frank was the editor of the place,” he said, “and I had every intention of working with him. But over the last couple of weeks, it became clear that Frank had very little interest or excitement about those changes, and I don’t think he would dispute that.” (Some former staff members disagree with Mr. Hughes’s timeline.)

Image Guy Vidra was recently hired as chief executive of The New Republic. Credit... Leigh Vogel/Getty Images for Yahoo! News

The changes, Mr. Hughes said, were prompted only by a desire to forge a sustainable business. “I don’t have expectations of this as the next Facebook. This is not the next enormous company,” he said. “But I do believe that the way to have institutions like this survive, the most reliable way, is to have them be sustainable, if not profitable, companies.”

He is disappointed to have lost many great journalists, he said, but he is optimistic about the future of The New Republic under Mr. Snyder. Mr. Hughes said he was not considering scaling back his investment in the magazine.