Dean Baquet, executive editor of The New York Times, criticized the Trump campaign’s move in a statement on Monday. “We condemn any action that keeps quality news media from reporting fairly and accurately on the presidency and the leadership of the country,” Mr. Baquet wrote.

At the same time, Bloomberg News’s approach to covering its owner’s candidacy has proved divisive.

Roughly 2,700 journalists work at Bloomberg L.P., the financial data company that is the wellspring of Mr. Bloomberg’s fortune, and this is not the first time that Mr. Bloomberg’s ambitions have placed his employees in an awkward spot. During Mr. Bloomberg’s 12 years as mayor of New York City, coverage of the billionaire’s wealth and personal life were considered off limits at Bloomberg News.

In a memo last month, Mr. Micklethwait acknowledged that “there is no point in trying to claim that covering this presidential campaign will be easy,” but added that the newsroom would continue to investigate Mr. Trump’s administration “as the government of the day.”

On Monday night, Mr. Trump, who had flown to London for a conference, added his own thoughts on the matter, deriding Mr. Bloomberg in a Twitter post as “Mini Mike Bloomberg” and describing Bloomberg News as a “third rate news organization.” (He also accused The Times of “hatred & bias.”) The president wrote that “It’s not O.K.!” for Bloomberg News to skip investigations of Democratic candidates.

While Bloomberg News has pledged to continue covering polls, policies and “who is winning and who is losing” the 2020 race, the prohibition against investigative reporting — considered among the most valuable forms of campaign journalism — has caused some uproar.

Megan Murphy, a former Washington bureau chief at Bloomberg News, wrote on Twitter that it was “staggering” for the news outlet to prevent “an army of unbelievably talented reporters and editors from covering massive, crucial aspects of one of the defining elections of our time.”

Marc Tracy contributed reporting.