The president, as he often does, has also focused on coverage of his response, complaining that he is being treated unfairly and blaming the news media. “If the virus disappeared tomorrow, they would say we did a really poor, and even incompetent, job,” he tweeted on Tuesday. “Not fair, but it is what it is. So far, by the way, we have not had one death. Let’s keep it that way!”

Before he took office, Mr. Trump was an outspoken critic of the Obama administration’s handling of the Ebola outbreak, arguing that infected people should not be allowed back into the United States.

Current Trump allies said the fact that the president chose to address the growing public health crisis quickly after returning from a trip to India showed how seriously he was taking the outbreak.

But privately, they say he has been reluctant to give in to what he has called an “alarmist” view of the virus’s potential to cause damage as he warily watches the effect of the outbreak on the stock market. He has been rattled by the Wall Street reaction to the spread of the virus in places like Italy, lashing out at the news media in tweets and accusing journalists of intentionally trying to harm the stock market.

And polls show that Mr. Trump’s credibility with much of the United States is low after an impeachment inquiry in which a majority of voters said they did not believe that he was telling the truth about his actions involving Ukraine.

Federal health officials had been bracing for the arrival of the virus in the country with minimal intervention by the White House.

As Ebola presented both a health and political threat to his administration in 2014, Mr. Obama carefully hewed to proven science, which he repeatedly invoked in his carefully calibrated public messages.