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South Africa risks turning into a "mafia state", a senior governing party official has warned, as pressure grows on President Jacob Zuma over his links with a wealthy family.

Gwede Mantashe made the comments after Deputy Finance Minister Mcebesi Jonas alleged the Gupta family had offered him a government promotion.

During a rowdy parliamentary session, Mr Zuma denied the family had influenced cabinet appointments.

The opposition called on him to resign.

Mr Mantashe is the third most powerful person in the governing African National Congress (ANC), and his remarks suggest Mr Zuma may be losing the confidence of influential members of the party as well, correspondents say.

Mr Zuma's presidency has been marred by allegations of corruption, cronyism and incompetence, amid a worsening economic situation.

The crisis deepened last Wednesday, when Mr Jonas said a member of the Gupta family had made "a mockery of our hard-earned democracy" by offering to promote him to the minister's job last year.

In an interview with Bloomberg, Mr Mantashe, the ANC secretary-general, said: "We need to deal with this; it will degenerate into a mafia state if this goes on."

He told the BBC Mr Zuma was not "untouchable", but denied that the party planned to oust him.

The ANC would, however, deal with the "corporate capture" of government, Mr Mantashe said.

Questioned by the opposition in Parliament about Mr Jonas' allegation, Mr Zuma said: "I'm in charge of the government. There is no minister who was ever appointed by the Guptas."

The Speaker ordered opposition Democratic Alliance (DA) leader Mmusi Maimane to leave the chamber for breaching parliamentary rules, prompting the party's MPs to walk out in solidarity with him.

Earlier, Mr Maimane said power had shifted from the government to the Guptas.

"You and your family are getting richer while South Africans are getting poorer," he told Mr Zuma.

The party said in a statement that Mr Zuma's position was becoming "increasingly untenable", and he should resign or be sacked by the governing party.

The left-wing Economic Freedom Fighters (EFF) party boycotted the parliamentary session, saying it did not recognise Mr Zuma as leader of South Africa.

The opposition has long accused Mr Zuma of letting the Guptas wield excessive influence.

The Guptas, who arrived in South Africa from India in 1993, have huge interests in computers, air travel, energy, and technology.

They said Mr Jonas' statement was political point-scoring.

In 2013, there was an outcry after a private jet carrying guests to the wedding of a Gupta family member was allowed to land at a South African military air force base in Pretoria.

The opposition has said that links between President Zuma and the Guptas were so close that they have been nicknamed the "Zuptas".