They fell more than 2% on Thursday, and closed down 0.8%, after the Financial Times said that Apple boss Steve Jobs got options without boardroom approval.
Apple's shares had fallen as much as 5% the previous session as more questions emerged over its stock-option policy.
An Apple spokesman said the firm was co-operating with an ongoing probe.
Held back
Apple was forced to delay the publication of its annual report due to an investigation by the Security and Exchange Commission (SEC).
The deadline for the document to be presented to the watchdog is Friday.
Apple is expected to restate some past results in light of the probe, which is looking into the so-called "backdating" of stock options for senior executives.
The company said in October that it had identified irregularities in relation to how it had accounted for stock options in the past but said no current staff were guilty of misconduct.
At the time, it highlighted the actions of two unnamed former executives, saying the way in which they recorded and accounted for stock options "raised concerns".
On Wednesday, a US online journal alleged that officials were looking at whether Apple altered documents to make options more valuable.
Apple did not comment on the reports in The Recorder, a legal publication owned by American Lawyer Media.
But spokesman Steve Dowling said it would provide the Department of Justice and the SEC with details of its own internal inquiry into allegations that options were manipulated to personally benefit senior staff.
Market pressure
Apple is one of more than 150 companies which are either the subject of federal investigations into stock option awards or conducting their own enquiries - and is not the only one about which allegations of falsification have been made.
Backdating refers to a process where stock options are linked to a point in time when a firm's shares were much lower, making them cheaper to exercise.
Despite tumbling in early trading on Wednesday, Apple shares recovered to close little changed by the end of the day's session.
However, the declines were renewed on Thursday, and Apple shares finished the session 0.8% lower at $80.88 in New York.
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