Sources from the palace informed Tolo News that medics from the Public Health Ministry have begun taking samples from other officials and staff members of the Presidential Palace after the cases were identified.
Doctors said there is a need for more test kits, as testing will slow the spread of the virus in the country.
"We will get the best results if we have enough kits," said Assadullah Esmat, head of the Infectious Diseases Hospital in Kabul.
"By testing more people, we can find patients who have the virus while it is in its incubation period," he added.
Nizamuddin Jalil, head of Kabul hospitals, a department of the Ministry of Public Health, said, "Our teams have increased in Kabul and they collect samples from anywhere they get a report, (of a suspected case)."
The Public Health Ministry on Friday reported 37 new cases of the coronavirus, bringing total cases to 521.
( With inputs from ANI )