The inquiry report, which Apple published last month, was deemed inadequate by investigators from the US Securities and Exchange Commission, the market regulator, and the Department of Justice.

Investigators were so unhappy with the results of the Apple inquiry that they called in Steve Jobs, Apple’s chief executive, for questioning last week.

The authorities’ chief complaint was that Apple had failed to describe adequately the procedure that it used to grant stock options to its executives.

The stock options debacle in Apple centred on options granted to Mr Jobs in December 2001. The award was backdated to October, when Apple’s share price was lower, thereby guaranteeing a much bigger profit for Mr Jobs if the options were ever cashed in.

Apple has admitted that it falsified records to show that a board meeting was held to approved the move when no such meeting took place. Apple also said that Mr Jobs was not aware of accounting implications of backdating and that he returned the options in order not to gain financially from the practice.

Apple is the most prominent of more than 150 options backdating cases under review in the United States. It is understood that investigation of the Apple case has been stepped up in recent days.

An SEC source said: “To have a representative from the Department of Justice — a criminal prosecutor — attend an interview with a company CEO is a very serious matter. This is not a polite request for information. The way the interview was conducted and the way the investigation seems to be moving forward [suggest] that Apple has a lot more explaining to do before the authorities will even begin to be satisfied.”

Apple declined to comment on the investigations.

The SEC source said that the investigating authorities would make no public statement, but said that the investigation was likely to go on for some time.

This week a pension fund, the New York City Employees Retirement System, was made lead plaintiff in a lawsuit against Apple, claiming that the options debacle had deprived Apple investors of share-price growth.

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