South Africa will crack down on groups behind xenophobic violence, President Cyril Ramaphosa said on Sunday, as anti-immigrant protests tarnish the country's reputation.

Ghana, Nigeria, Malawi and Mozambique are repatriating some of their citizens caught up in the protests, which have sometimes turned violent. Mozambique has said five of its citizens were killed.

"We will act against forces who are exploiting the concerns of our people about illegal immigration to further their own political, personal and criminal agendas," Ramaphosa said in a televised address, without specifying the actions.

"We will and must not allow groups to use the legitimate concerns of South Africans to destabilise our country through inciting lawlessness and violence," he said.

He cautioned citizens against stopping people on the streets to demand their identities, and said enforcement of immigration laws was a responsibility solely for the state.

Xenophobic attacks are a recurring problem in South Africa, where immigrants are often blamed for economic woes such as high unemployment and crime. Defenders of migrants say such accusations are unfair and exploited by populist politicians.

Ramaphosa said migrants were being blamed for problems that had arisen because of poverty and high unemployment.

The government was taking measures to address migration, including stricter enforcement of regulations, an overhaul of laws, and working with other countries to address the root causes of illegal immigration, he added.

He noted plans for policies including setting up dedicated courts to deal speedily with immigration cases, and upgrading the paper "green book" identity documents carried by South Africans and legal migrants, which are being replaced with more secure, biometric digital ID cards.

Ghana has petitioned the African Union over South Africa's treatment of Ghanaians there, its Foreign Minister Samuel Okudjeto Ablakwa said on Saturday. It was compiling a list of assets lost by Ghanaians because of attacks in South Africa, for future use in any litigation.