Minister of Health Dr Zweli Mkhize said it was premature to talk of travel bans at the moment - a strategy that has been announced by some countries such as Saudi Arabia, which banned travel to or from countries such as Italy and China.
Mkhize said testing for the virus had been conducted on international travel lots coming into South Africa and not on domestic travelers.
The department of Health has called for calm as more were being conducted on those who showed systems.
The government as put in place a ministerial task team which includes the departments of international relations and home affairs which will deal with avenues on how to tackle the Coronavirus.
Earlier on Monday, the Health department has confirmed that four more people have tested positive for the Covid-19 Coronavirus.
This brings the total number of people who tested positive for the virus to seven.
The Coronavirus, which emerged in the Chinese city of Wuhan in December, has spread quickly around the world. Italy has confirmed the highest infections and deaths in Europe.
South Africa confirmed its first case of the virus last week when a 38-year old man from KwaZulu-Natal had tested positive for the virus after he began suffering symptoms.
He is currently under quarantine in a KZN hospital. The man’s wife also tested positive for the virus over the weekend along with a Gauteng woman.
A Sandton school, Grayson Preparatory, was shutdown on Monday when one of its employees appeared to show symptoms similar to the virus.
Mkhize said the health department and the National Centre of Disease Control (NCDC) we’re not surprised by the cases confirmed because all the individuals were part of a group of ten people who had traveled to Italy and returned to the South Africa on March 1. The group consisted of ten people.
A 45-year old man was tested positive for the virus in KwaZulu-Natal, while a suspected case in the North West has returned negative.
Mkhize said health officials were now working on tracing all the individuals , whom they refer to as “contact individual”, who may have interacted with the group of individuals.
All those who have tested positive were being quarantined in public hospitals.
The minister said all those who had come into contact with the individuals should avail themselves for testing.