President Thabo Mbeki announced yesterday that a panel had been set up to look into xenophobic attacks.
He was speaking as a fresh wave of violence swept through Johannesburg - with five people reported killed in Cleveland yesterday.
Speaking in Pretoria, ANC president Jacob Zuma also condemned the attacks on foreigners.
Johannesburg Metro police warned people to avoid dangerous CBD areas.
Speaking at San Lameer after a meeting of the International Investment Council, Mbeki said it was important for the police to act firmly.
"We hope the panel and police will work together and help us get answers to who is behind this," Mbeki said.
People could not be allowed to go around beating up other people, he said.
Zuma said: "We cannot allow South Africa to be famous for xenophobia. We cannot be a xenophobic country."
He said he could not understand how people could attack foreigners when ANC members had sought refuge in neighbouring countries.
Metro police spokesman Wayne Minnaar said on SABC radio that motorists should avoid certain CBD areas.
In Hillbrow there was a heavy police presence after residents pounced on foreigners selling goods on the streets, police spokesman Govindsamy Mariemuthoo said.
Speaking on Zimbabwe, Mbeki said it was important that the coming June 27 election was free and fair for all.
"People must be able to choose a leader freely."
He said a team had been sent to Zimbabwe to deal with issues of conflict and violence.
"We placed them there to stop the violence," - Sapa