The rumor appeared shortly after the new coronavirus struck China and spread almost as quickly: that the outbreak now afflicting people around the world had been manufactured by the Chinese government.

The conspiracy theory lacks evidence and has been dismissed by scientists. But it has gained an audience with the help of well-connected critics of the Chinese government such as Stephen K. Bannon, President Trump’s former chief strategist. And on Sunday, it got its biggest public boost yet.

Speaking on Fox News, Senator Tom Cotton, Republican of Arkansas, raised the possibility that the virus had originated in a high-security biochemical lab in Wuhan, the Chinese city at the center of the outbreak.