“It makes a huge difference if it was Wuhan or Beijing,” said Michael Pillsbury, a China scholar at the Hudson Institute who informally advises Mr. Trump.

Michael Pillsbury, a Hudson Institute scholar who has spoken to Mr. Trump on China, noted that previous administrations have also had internal divisions on how hard to challenge Beijing. “It’s not a Cold War 2.0 relationship,” he said. “It’s more cooperative than that.”

Michael Pillsbury, an informal China adviser to Mr. Trump, said the S.E.C. often makes the logical argument that Chinese companies would simply choose to list on exchanges in other countries.

“President Trump is demanding to know the origins of the virus and what Xi Jinping knew when about the cover-up,” Mr. Pillsbury said.

Other ideas are also being discussed, said Michael Pillsbury, a Trump adviser and director of the Hudson Institute’s Center on Chinese Strategy, including whether Chinese access to the big American platforms of YouTube, Twitter and Facebook could be limited. (The platforms are blocked in China, but are powerful vehicles for Chinese propaganda globally.)

The two countries already are working together behind the scenes. Michael Pillsbury, a senior fellow at the Hudson Institute who advises the Trump administration on China, pointed to efforts underway by the American biotechnology companies Inovio Pharmaceuticals, GeoVax and Gilead Sciences to develop a coronavirus treatment in China, some in partnership with Chinese companies.