The health department does not know how many cases exist at nursing homes and assisted-living facilities, Dr. González said. Over the next three weeks, the department plans to do antibody testing at some 28,000 residents and 9,000 staff at 1,000 long-term facilities.

The youngest person to die so far has been a 29-year-old man identified by his father as Joshua James Sánchez. He went to the emergency room twice with symptoms and was denied a test until the third time, when he was already in respiratory distress, his father, Luis Ángel Sánchez, wrote on Facebook. The elder Mr. Sánchez wrote that his own father also succumbed to the virus.

“You cannot understand this pain unless you experience it,” he wrote. “And I don’t wish this disastrous experience on anybody.”

Michelle García Mercado, a 23-year-old college student from Caguas, said her father struggled to get tested after learning that a co-worker had tested positive. Her father first had to test negative for flu and bacterial pneumonia.

“They told him to stay home,” she said.

Her father got a test only after coming down with body aches. While they awaited the results, Ms. García, who helps care for her grandfather and feared she might be a virus carrier, tried to get tested herself but was turned away because she did not have symptoms. Her father’s result came back negative.

Frustration over the slow testing has prompted some Puerto Ricans to protest from their balconies with pots and pans and from their cars in drive-by caravans. On social media, they address the governor with #WandaLasPruebas, demanding more tests. Some of the same activists led the protests that ousted former Gov. Ricardo A. Rosselló last summer.

“People are tired already of sitting at home without clear information,” said Zoan Dávila, 31, a lawyer from Cayey who is a member of the Colectiva Feminista en Construcción, which organized a protest last week. “They don’t trust the state and what it is doing.”