Dr. Anthony Fauci has been accused by critics of lying after newly released documents appear to contradict his claims that the National Institute of Health did not fund gain-of-function research at China’s Wuhan lab.

Senator Rand Paul led the criticism against Fauci on Tuesday after the documents, obtained by The Intercept, detailed grants given to EcoHealth Alliance — the nonprofit that funneled federal funds to the Wuhan Institute of Virology for bat coronavirus research.

Included in the trove of documents is a previously unpublished grant proposal that EcoHealth Alliance, which is run...