Police were sent to break up 3,000 miners - some armed with clubs and machetes - who had gathered on a hillside overlooking Marikana to call for a pay rise of about $1,000 (£636) a month.
South African President Jacob Zuma has announced an inquiry into violence at a mine in the north-east of the country, calling the deaths there "tragic".
Thirty-four people were killed when police opened fire on striking platinum miners on Thursday.
At least 78 people were injured in the confrontation.
Mr Zuma, who cut short a visit to Mozambique to visit the scene, said he was "saddened and dismayed" at the "shocking" events.
"I am convinced that the Commission of Inquiry will uncover the truth and facts will emerge," he said in a statement after meeting police and injured workers.
Visibly distraught, he said it was not a time for finger-pointing but he would try to make sure such a loss of life never happened again.
The president said it was a "cornerstone of hard-won democracy" to allow for peaceful protests adding that it was now "a day for us to mourn together as a nation - a day to start rebuilding and healing".
The violence took place at a platinum mine in Marikana, owned by Lonmin.
The BBC's Milton Nkosi in Johannesburg says South Africans are shocked and bewildered by what happened - 18 years after the end of the brutal system of apartheid.
Wives of the missing miners have been frantically searching for their loved ones, he says.
Some of them were chanting on Friday an old song from the anti-apartheid struggle in the Xhosa language: "What have we done, what have we done to deserve this?"
They wanted to know why the police used such force against protesters who were mostly carrying machetes, spears and clubs.