The police believe it would be foolish to assume that there was no longer a threat from bombers who targeted Soweto last week.
"We are working on the side of caution," Director Sally de Beer, spokesperson for national Commissioner Jackie Selebi, said on Sunday.
"There is no need for people to panic, but they should be vigilant and report anything suspicious to the police immediately. We are confident that the situation is under control," she added.
Police have been on high alert since a string of explosions ripped through Soweto during the early hours of Wednesday morning, with a 10th blast damaging a Buddhist temple in Bronkhorstspruit outside Pretoria shortly before midday.
It is understood that right-wing extremists are behind the terror campaign.
The Sunday Times reported on Sunday that other right-wing suspects had compiled a hitlist targeting former president F W de Klerk, former ministers Pik Botha and Roelf Meyer, retired Freedom Front leader Constand Viljoen and a Tshwane councillor. The men were said to be viewed by extremists as having sold out their people.
However, police are confident they know the identities of those responsible for last week's Soweto blasts.
De Beer said police had positively identified "a grouping of people" behind the explosions, and "investigations in that direction are going well".
She said she couldn't discuss details because arrests still had to be made.
- Police have warned that anyone caught making a hoax bomb threat will be severely dealt with.
Perpetrators can face a jail term of between five and 15 years without the option of a fine if convicted.
Michael John Smith, 33, was arrested on Thursday and faces charges for making a bomb threat.
He was arrested at a pub in Germiston after allegedly telling patrons he planted the Soweto bombs.
In another incident, a doctor was arrested at Johannesburg International Airport after making a "joke" about having a bomb, knives and scissors in his possession last week. He has been granted bail and will appear in a Kempton Park court next month.
The police were also entitled to a civil claim to recover the costs involved in unnecessarily sending out reaction teams, and this could amount to thousands of rands, said De Beer.
"We intend regaining everything we lost in terms of wasted man-hours and resources," she added.