About 5,800 people who have been administered COVID-19 vaccines in the U.S. have still been infected anyway, the U.S. Centers for Disease Control and Prevention (CDC) said on Thursday.

So far, about 5,800 so-called "breakthrough" cases have been reported to the CDC, U.S. media quoted the agency as saying.

Vaccine "breakthrough" infections make up a small percentage of people who are fully vaccinated, less than one percent, according to the CDC.

Among the 5,800 "breakthrough" cases, some became seriously ill and 74 people died, CNN quoted the CDC as saying. Meanwhile, 396 cases, seven percent of those who got infected after they were vaccinated, required hospitalization.

The health agency called on all eligible people to get a COVID-19 vaccine as soon as possible and urged fully vaccinated individuals to keep up precautions, such as wearing masks and social distancing, to avoid contracting the disease.