People fully vaccinated against COVID-19 should be tested for the virus if they come into contact with infected people, whether or not they have symptoms, say updated testing guidelines from the U.S. Centers for Disease Control and Prevention.

The agency previously said that fully vaccinated people did not need to be tested after exposure to the virus unless they had symptoms, The New York Times reported.

Fully vaccinated people should wear a mask in public indoor spaces after exposure, the agency said. Three to five days later, they should be tested. If the results are negative, they can stop wearing masks indoors. If the results are positive, they should isolate at home for 10 days, the guidance states.

The new testing advice was released Tuesday, the same day the CDC issued new mask guidelines that recommend that the fully vaccinated wear a mask indoors if they live in a high-transmission area.

The agency also recommended that vaccinated people in close contact with unvaccinated people, including children under 12, consider wearing masks in public indoor spaces whatever the transmission rates in the local community. In a shift, the agency also recommended universal masking in schools.

"Our updated guidance recommends vaccinated people get tested upon exposure regardless of symptoms," CDC director Dr. Rochelle Walensky told the Times. "Testing is widely available."

Even though fully vaccinated people may still get infected, people with these "breakthrough" infections tend to have mild or no symptoms because vaccines provide strong protection, according to the Times.