Mr. Pichai noted in a memorandum on Thursday that Verily was "part of our Alphabet family" and help in the next "days and weeks" to respond quickly. He added a link to the form, and employees could volunteer to help. The next day, more than 1,700 people signed the agreement, and that number has been passed on to Mr. Kushner's team.

Last Friday, inspired by the stock market crash and warnings from health experts about the 's rapid spread, arranged an afternoon press conference.

A few hours before the president became president, Mr. Kushner's team prepared a poster showing how the site works; it did not specifically mention Google, but the flowchart showed that "screening sites" could be used across the country Consumers offer "new options for consumers" when they look for infections.

At the press conference, Mr. Trump was very enthusiastic.

"I want to thank Google-Google is helping to develop a website," he said. "Unlike past websites, this will be done soon to determine if testing is needed and to facilitate testing in a convenient location nearby."

Moments later, at the invitation of Mr. Trump, Dr. Deborah L. Birx, who is coordinating the response to the virus, raised a Kushner poster, saying it represented "a new test method that will be screened The site started here, powered by Google. "

Initial response in Silicon Valley, 3,000 miles away, was quick.

Trump's comments took Google completely by surprise, and executives issued a statement Friday afternoon to alleviate expectations, which clearly shows that the site is headed by Verily, not Google itself. Verily spokeswoman Carolyn Wang said the plan was to establish a pilot site to test the Bay Area location, but did not provide a timeline for wider deployment.

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According to a government official, Mr. Kushner and Mr. Pichai spoke about the site for the first time on Friday night.