One of the two persons drives the vehicle of a joint secretary-level officer posted in the finance department, while the other driver works for a senior police officer. Both of them tested positive for the disease on Thursday.
The finance department is located on the 12th floor of the 14-storey building.
Following this, attendance was slim at the secretariat, especially in the departments located on the 10th, 11th, 12th, 13th as well as in Chief Minister's Office (CMO) on the top floor, on Friday, he added.
"Now, the joint secretary-level officer has met several people during all these days. We have to identify them and sent them for isolation. People who came in touch with the two drivers and the officials for whom they work, have been directed to go for isolation," the source said.
The two officials concerned were asked to go for home isolation while the drivers were sent for treatment.
People are being allowed in the 14th floor "only for very very important reasons", sources at the CMO said.
"As part of the precautionary measures, entry to the chamber of the chief minister was restricted even to senior officers," the source said.
Most officials have been asked to speak on intercom, and employees are coming on shifts to avoid crowding and maintain social distancing.
Last week, drivers of two senior officials posted at the CMO had tested positive for the disease following which the entire building was sanitized for two days.
After that, employees including senior officials on the 12th, 13th and at the CMO were tested for the contagion.
Earlier in the day, Banerjee had urged people to avoid crowding in buses and asked private firms to allow grace timing for employees reporting for work.
"We've ensured no one's marked late in government offices. Visit public places only when it is urgent. Always wear masks and stay safe!" Banerjee tweeted. SCH NN NN