Guptas deny meeting South Africa's Mcebisi Jonas

Mecebisi Jonas says he was offered $45m by Ajay Gupta

The wealthy family at the heart of South African corruption allegations has denied meeting a top politician, who said he was offered a bribe.

An investigation by South Africa's anti-corruption body suggested the Gupta family exercised political influence over President Jacob Zuma.

One witness, Deputy Finance Minister Mcebisi Jonas, said Ajay Gupta offered him money to accept a promotion.

The Guptas welcome a proposed public inquiry in order to "clear our name".

"Our cursory reading of [the report] shows the evidence gathered is riddled with errors and is subject to rebuttal," a statement from the family says.

For example, it says Mr Gupta "never met with Deputy Minister Jonas".

The report's author, former Public Protector Thuli Madonsela, recommended the establishment of a judicial commission to look into her evidence within 30 days.

• The Guptas and their links to Zuma

• South Africa's corruption crusader

She was looking into allegations that Mr Zuma had an improper relationship with the wealthy businessmen.

President Jacob Zuma is under pressure to resign after the publication of the report

The Guptas' lawyer, Gerd van der Merwe, told the BBC that Ms Madonsela did not give his clients the chance to present their evidence during her investigation.

He said the family now wants to be part of the process.

The deputy finance minister is quoted in the report as saying that Mr Gupta offered him 600m rand ($44.6m; £36.2m) last year, "to be deposited in an account of his choice", if he accepted the post of finance minister.

Mr Gupta also asked him if he had "a bag which he could use to receive and carry 600,000 rand in cash ($44,400) immediately", Mr Jonas alleged, adding that Mr Zuma's son, Duduzane, was present at the meeting.

Mr Jonas said he did not accept the money.

He was expected to remove key Treasury officials from their posts and advance the Gupta family's "business ambitions", Mr Jonas is quoted as saying.

Another allegation that Ms Madonsela explored was that Brian Molefe, head of the state power company Eskom, deliberately weakened the financial position of one of its suppliers, Optimum Coal, thereby allowing the Guptas to buy it up.

Her report says that there were 58 phone calls between Mr Molefe and Mr Gupta.

Also, using mobile phone records, it places the Eskom boss near the Gupta family home on 19 occasions during the period that the Optimum Coal deal was being discussed.

Eskom CEO Brian Molefe has said he wants a chance to give his version of events

In a tearful press conference on Thursday, Mr Molefe denied the allegations and complained that he never had the opportunity to give his side of the story, the News24 website is reporting.

The Guptas say that the evidence about the Optimum deal is "flawed".

The 355-page report by Ms Madonsela is entitled "State of Capture" and is illustrated on its front page with a hand strung with puppet wires.

The president has been dogged by corruption allegations for more than a decade, but has repeatedly denied any wrongdoing.