The Gupta brothers have come under fire for wielding immense power behind the scenes over Jacob Zuma and ministers in his government. (File photo)

South Africa's wealthy Gupta family, accused of exerting undue influence over President Jacob Zuma, have left country for Dubai, a newspaper reported Sunday."The whole family is in the process of leaving," family spokesman Nazeem Howa told the City Press weekly.The paper said that Ajay and Atul Gupta, two brothers from the family of wealthy Indian immigrants who own a vast business empire with interests in mining, media, technology and engineering, were seen on Thursday evening at a Johannesburg airport boarding their private jet for Dubai.One of their wives was with them as well as five assistants, with the party boarding the plane "with enough luggage for 20 people," a witness told the paper.On Friday, the family released a statement saying they were stepping down from the leadership of Oakbay Investments, a holding company with interests ranging from mining to media, in a move linked to the closure of the firm's accounts by two major banks."It is with deep regret that, following a period of sustained political attack on the Gupta family and our businesses... we have come to the conclusion that it is time for the Gupta family to step down from all executive and non-executive positions," the letter said."This follows the unexplained decisions by several of our banking partners and our auditors to cease working with us, and the continued press coverage of false allegations."The closure of the bank accounts had made it "virtually impossible to continue to do business in South Africa," said the letter, which was signed by Howa, Oakbay's chief executive.In recent weeks, this family, who moved to South Africa in the 1990s, has come under fire for wielding immense power behind the scenes over Zuma and ministers in his government.Persistent rumours of the family's excessive influence over the president took concrete form in March when evidence emerged that they allegedly offered key government jobs to those who might help their business interests.Zuma, whose second presidential term ends in 2019, has also faced scathing criticism over his friendship with the Gupta family, with their relationship providing ammunition for the government's fiercest critics.The Guptas arrived in South Africa in 1993 as white-minority apartheid rule crumbled and a year before Nelson Mandela won the country's first democratic elections.As the country opened up to foreign investment, the Guptas -- previously small-scale businessmen in India -- began to build their sprawling empire.They also developed close links with the ruling African National Congress (ANC) party, and particularly with Zuma, well before he became president in 2009.