WASHINGTON—President Trump isn’t firing Anthony Fauci, the White House said Monday, seeking to extinguish speculation that flared over the weekend after Mr. Trump retweeted a critic who called for the member of his administration’s coronavirus task force to be dismissed after he said lives could have been saved if the government had acted more quickly.

“Today I walk in and I hear I’m going to fire him. I’m not firing—I think he’s a wonderful guy,” Mr. Trump said of Dr. Fauci at a White House news conference later Monday.

...