President Cyril Ramaphosa says the government will assess the effectiveness of the 21-day lockdown, which is due to end on 16 April, in the coming days.
He was speaking on the sidelines of his visit to the National Water Command Centre at Rand Water in Johannesburg.
Ramaphosa was joined by Human Settlements Minister Lindiwe Sisulu at the command centre, where they held virtual meetings across several provinces and municipalities.
Ending SA's Covid-19 lockdown too soon will be a death warrant for many
Speculation has been rife the lockdown would be extended beyond three weeks, with growing concern over the impact of such a decision on an already ailing economy.
"Of course, it impacts on the economy negatively, but it is important to save lives, because lives are important and the lives of our people matter," said Ramaphosa.
"The economy will take a real knock, but we will come up with strategy and how we move our economy forward."
He added the greatest challenge during this period was getting everyone to abide by the regulations.
Ramaphosa also used the moment to defend the decision to go into lockdown, describing it as one of the most important measures taken by his government in fighting the spread of Covid-19.
"What I can say if we had not locked down South Africa as we have, I can tell you without any shadow of a doubt the infection rate would have been a lot, lot higher than what we have."
He also indicated he had summoned Communications Minister Stella Ndabeni-Abrahams to a meeting to discuss a purported social media post of her having lunch with former deputy higher education minister Mduduzi Manana.
The picture posted by Manana on Instagram has sparked debate on whether the minister failed to comply with the country's lockdown regulations.
The post has since been taken down.