Ajay and Atul Gupta File picture: Independent Media

The FBI has opened an investigation into US links to the Guptas, escalating a scandal over the family's alleged use of a friendship with President Jacob Zuma to control state businesses, the Financial Times said on Thursday.

The newspaper, which cited "people familiar with the matter", said US investigators had been looking at individuals, bank accounts and companies in the US for ties to alleged graft involving the family. 

It gave no further details.

The Gupta family and Zuma have denied any wrongdoing.