A federal appeals court has refused to stay an order that imposes an antitrust monitor on Apple, despite the company’s complaints that the monitor has been conducting an illegal roving investigation.

In a ruling published on Monday, the Second Circuit Court of Appeals wrote that the dispute came down to a disagreement over what the monitor was empowered to do, and adopted the Justice Department’s position that the monitor was limited to verifying whether Apple was informing its employees about their duty to comply with an anti-trust order from last year.

The original order imposing the monitor came as part of a larger decision last year in which a New York federal judge concluded that Apple had violated antitrust laws by brokering an illegal conspiracy with publishers to fix the price of ebooks.

Apple, which is appealing the overall decision, has accused the monitor, Michael Bromwich, of starting his duties…