“We are asking the American public to work with us to prepare, in the expectation that this could be bad,” Dr. Messonnier said.

Shortly after the news conference, stock markets plummeted for the second day as investors dumped stocks and turned to the safety of government bonds. The S&P 500 fell by more than 3 percent, following a 3.4 percent slide on Monday — the worst day for the American markets since February 2018.

In contrast to his own health officials, President Trump, traveling in India, played down the threat, saying, “You may ask about the coronavirus, which is very well under control in our country.”

“We have very few people with it, and the people that have it are, in all cases, I have not heard anything other — the people are getting better, they’re all getting better.”

As of Tuesday, the United States has just 57 cases, 40 of them connected to the Diamond Princess, the cruise ship overwhelmed by the coronavirus after it docked in Japan. Those patients are in isolation in hospitals, and there are no signs of sustained transmission in American communities.