Cyril Ramaphosa said a third of the country’s more than 22,000 cases had been recorded in the last week.
Despite that, the president said the current lockdown could not be sustained indefinitely.
He announced that, from 1 June, more restrictions would be lifted.
Mr Ramaphosa was speaking after a mining company in South Africa said 164 workers at a gold mine near Johannesburg had tested positive for Coronavirus.
There have so far been 429 recorded Covid-19 deaths in the country.
How will the lockdown measures be eased?
An overnight curfew will no longer be in place, more businesses will be allowed to open and schools will re-start, the president said.
A controversial ban on alcohol will also end with limited sales allowed for home consumption only. A ban on the sale of cigarettes will remain.