WASHINGTON—Acting Navy Secretary Thomas Modly resigned on Tuesday following an uproar after he excoriated the former captain of the aircraft carrier Theodore Roosevelt, whose crew had become stricken with the coronavirus, according to U.S. military officials.

Mr. Modly was under pressure to resign after an extraordinary chain of events over the last two weeks that has plunged the Navy into disarray as it scrambles to respond to the Covid-19 crisis, the officials said.

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