President Zuma promised a thorough investigation of the shootings when he visited the mine on Wednesday
'We are so angry'
Events are taking place across South Africa to remember the 44 people killed in recent violence at the north-western Marikana platinum mine.
A prayer service at the Lonmin-owned mine was to be followed by a memorial service attended by members of the cabinet.
Reports of worker action at two other platinum mines have added to industry fears the unrest is spreading.
The price of platinum has leapt to its highest since May.
A week ago, 34 miners died when police opened fire at the Lonmin-owned mine, where workers were on strike to demand higher pay.
Previously 10 people, two of them police officers, had died in violent clashes.
The mine has been closed as a result of the unrest.
Politicians, religious leaders, workers and members of the local community are attending a memorial service at a church near the mine to commemorate all those who have died in the violence.
Among those attending the service, at the Nkangeng Informal Settlement, are the head of President Jacob Zuma's office, Collins Chabane.
Early on Thursday, a traditional prayer service was held to ritually cleanse the spot where the 34 strikers were shot dead by police.
The deadly clashes have thrown South Africa into a frenzy of outrage and grief, says the BBC's Nomsa Maseko at the mine.
President Zuma has rejected criticism that his handling of the situation hurt investor confidence, adding that he is confident that South Africa is in control of the situation.
But fears expressed by analysts and industry executives that unrest could spread to other parts of the mining sector were given weight with reports of worker action at two other platinum mines.
The world's top platinum producer, Anglo American Platinum, said it had received a broad list of demands from its South African workers.
Meanwhile, some 500 workers at a shaft in the nearby Royal Bafokeng Platinum downed tools demanded a pay increase and reportedly blocked fellow miners from going to work.
Visiting the Marikana mine on Wednesday, Mr Zuma told workers he "felt their pain" and promised a thorough investigation of the shootings.
But correspondents say the mood at the meeting was subdued, and did not feature the cheering and ululating that usually greets the president.
Some of those present chanted "down with the police".
Religious leaders have brokered talks between the Lonmin management and workers in an attempt to break the deadlock in the dispute over pay.
On Tuesday, Lonmin dropped its threat to fire workers if they failed to end their strike after many workers ignored the ultimatum. The company says the strike is illegal.
Police said they opened fire last week because strikers wielding machetes and clubs had refused to lay down their weapons.
The striking miners say they are currently earning between 4,000 and 5,000 rand (£305-£382: $486-$608) a month and want their salary increased to 12,500 rand.
The company says most workers are paid about 10,500 rand, if bonuses are added.
Industrial conflict over pay appeared to be spreading to other mines in South Africa on Wednesday, with about 600 workers at the nearby Royal Bafokeng Platinum Mine also going on a strike to demand higher wages.