President Cyril Ramaphosa "condemned in the strongest terms" the violence that erupted in Johannesburg on Sunday which claimed two lives, saying it was a "crime against our prosperity".
Ramaphosa also expressed his condolences to the families of two people who were reportedly stabbed and shot – the latter incident involving a large group of armed attackers, according to a statement from the Presidency on Monday.
News24 earlier reported that a group of men, some of them wielding sticks, pangas and tree branches, marched through the city centre after disrupting a meeting in which IFP president Emeritus Mangosuthu Buthelezi spoke following last week's deadly xenophobic violence.
One person was stabbed on the corner of Bree and Plein streets.
As the violence spilt over to Malvern, another person was shot dead on Sunday night.
Ramaphosa called on law enforcement agencies to maintain vigilance and firmness in dealing with people or groups who took the law into their own hands and violated the dignity rights of people without raising grievances with the relevant authorities.
He applauded law enforcement agencies for arresting at least 16 people during Sunday's operations to bring calm and order to Johannesburg.
"Government will not allow sporadic lawlessness and violence to disrupt the safety and livelihoods of millions of South Africans and the majority of foreign nationals in our country who are law abiding and have the right to conduct their lives and businesses in peace," he said, according to the statement.
"Lawlessness, injury and death inflict a great psychological and economic cost that lasts long after victims are buried, arrests are made and streets are cleared. This cost holds back our country and undermines all the efforts we are making to grow a South Africa that offers opportunity to all who live in it.
"Lawlessness is a crime against our prosperity and stability as a nation, and those who want to upset our public order must expect to face the gravest impact of the law."
The violence has left many shops in Johannesburg plundered. South African businesses operating in other countries of the continent, notably Nigeria, have reported a backlash in the past week.
Several leaders of other African countries also condemned the xenophobic violence.
Also on Monday, Minister of International Relations and Cooperation Naledi Pandor was expected to meet with African ambassadors in Pretoria.
On Tuesday, the National Assembly is expected to have an urgent debate on the "recent incidents of violence and criminality in the country, including those affecting foreign nationals".