Thousands of emails have emerged in the local press exposing alleged misconduct over lucrative government contracts.
Thousands of emails have emerged in the local press exposing alleged misconduct over lucrative government contracts awarded to the Guptas, an influential Indian business family.
Zuma has been under growing pressure to resign from senior ANC figures, trade unions and business leaders, as well as from tens of thousands of marchers at a series of street demonstrations.
"These reports contain very worrying claims about the nature of the relationship between government and private interests," the ANC said in a statement.
"The African National Congress calls on government to urgently seek to establish the veracity of these claims and explanation from those implicated."
One apparent deal revealed by the emails alleged that the government assisted the Guptas in making a 5.3 billion rand ($410 million) profit from a procurement deal to buy trains from China.
Other allegations suggest the Guptas helped Zuma's son Duduzane to buy a $1.3-million flat in Dubai, and that the president -- who faces multiple court cases in South Africa -- was seeking residency in the city.
A state ombudsman report last year called for prosecutors to investigate accusations that Zuma allowed the Guptas to have undue influence over government, including letting them choose ministers.
Brian Molefe, a close ally of Zuma, resigned as Eskom chief after being implicated in the ombudsman report.
He was re-appointed this month but soon removed from the post again as Zuma's government struggled to react to the developing controversy.
The president, 74, has survived a string of scandals, but faces increasing criticism as the South African economy stalls and after the ANC suffered unprecedented losses in local polls last year.
The Gupta family -- brothers Ajay, Atul and Rajesh -- built an empire in mining, transportation, technology and media after arriving in South Africa in the early 1990s.
Zuma, who came to office in 2009, is due to step down as head of the ANC in December, and as national president ahead of the 2019 general election.
He is seen as favouring his ex-wife, former African Union chief Nkosazana Dlamini-Zuma, to succeed him.
Zuma brushed off criticism in parliament on Thursday, while the Guptas deny all wrong-doing.