WASHINGTON — The Trump administration is racing to contain an outbreak of the coronavirus inside the White House as some senior officials believe that the disease is already spreading rapidly through the warren of cramped offices that make up the 3 floors of the West Wing.

Three top officials leading the government’s coronavirus response have begun two weeks of self-quarantine after two members of the White House staff — one of President Donald Trump’s personal valets and Katie Miller, the spokeswoman for Vice President Mike Pence — tested positive.

“It is scary to go to work,” Kevin Hassett, a top economic adviser to the president, said.

The discovery of the 2 infected employees has prompted the White House to ramp up its procedures to combat the coronavirus, asking more staff members to work from home, increasing usage of masks and more rigorously screening people who enter the complex.

Late Sunday, the White House put out a statement saying that Pence would not alter his routine or self-quarantine. Trump continues to reject guidance from the Centers for Disease Control and Prevention to wear a mask when meeting with groups of people. Two senior administration officials said there were no plans to keep Trump and Pence apart because of a concern that they both could be incapacitated by COVID-19.

Concern about the spread of the virus in the White House has temporarily sidelined three of the most high-profile members of the coronavirus task force: Dr. Robert Redfield, director of the Centers for Disease Control and Prevention; Dr. Stephen Hahn, commissioner of the Food and Drug Administration; and Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases.

Redfield and Hahn announced over the weekend that they would self-quarantine for 2 weeks after coming in contact with an infected member of the president’s staff. Both attended a meeting in the Situation Room last week where Miller was present, and they said they would continue to participate in the response effort from home. Fauci said he, too, had begun a “modified quarantine” after what he called a “low-risk” contact with an infected staff member.

Sen. Lamar Alexander, R-Tenn., said that all three doctors would participate Tuesday by videoconference in a previously scheduled hearing on the virus response and efforts to reopen the economy.

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