The chair of Tesla’s board of directors denied a report that the company had begun to look for a replacement for Elon Musk, the chief executive who has been spending much of his time working for President Trump while the automaker’s sales and profits plummet.

Robyn Denholm, who has led the board for more than six years, said on X that the report in The Wall Street Journal was “absolutely false.”

“The CEO of Tesla is Elon Musk and the board is highly confident in his ability to continue executing on the exciting growth plan ahead,” Ms. Denholm said on Tesla’s account on X, the social media firm owned by Mr. Musk.

The Journal reported late Wednesday that, about a month ago, the Tesla board had contacted executive search firms to help look for Mr. Musk’s replacement, citing “people familiar with the matter.”

After the company reported a 71 percent drop in quarterly profit last week, Mr. Musk promised to spend more time at Tesla and less time in Washington. He said that he would spend one or two days a week on administration work.

Mr. Musk’s absence from Tesla while he oversaw Mr. Trump’s efforts to slash government spending and cut federal government jobs has become a sore point with investors. Mr. Musk’s involvement with the administration and with right-wing causes in Europe has prompted protests at Tesla dealerships and is partly responsible for a steep drop in sales. Electric vehicle buyers tend to be liberals or centrists.

Tesla’s revenue fell 9 percent in the first quarter of the year, to $19.3 billion, the company reported last week.

The automaker has lost market share in the United States, China and Europe as competitors like BYD, General Motors, Volkswagen and other companies introduce dozens of electric models. Analysts have faulted Tesla for failing to expand its lineup beyond two main cars.

The Model Y sport utility vehicle and the Model 3 sedan account for a vast majority of Tesla’s sales. The Cybertruck, Tesla’s newest vehicle, has not sold as well as Mr. Musk said it would.