The European Commission has begun an investigation whether Apple has broken competition rules.
One investigation centres on iPad and iPhones being limited to installing apps from Apple’s own App Store, among other restrictions imposed on third-party developers.
And the other involves Apple Pay, with one issue being that other services cannot use the iPhone’s tap-and-go facility.
Apple said it was “disappointing” the EU was “advancing baseless complaints”.
And it accused companies that had raised allegations against it of wanting a “free ride”.
“Our goal is simple: for our customers to have access to the best app or service of their choice, in a safe and secure environment.”
Apple is also under scrutiny in the US where the House Judiciary Committee is reported to have asked for its chief executive Tim Cook to appear alongside other tech leaders to answer questions about anti-trust concerns.
Amazon has said that its chief executive Jeff Bezos is willing to testify, so long as Mr Cook and his counterparts at Facebook and Google also give evidence.
The latest development comes days before Apple holds its annual developers conference.
The investigation into Apple’s App Store stems from a complaint raised by the music streaming service Spotify.
The European Commission has concerns about the conditions imposed on services that have added the facility.
It also has reservations that alternative payment tech cannot make use of the near field communication (NFC) chips in Apple’s products to work with contactless payment terminals.
By contrast, Samsung phones – for example – let their NFC chips be used for both Samsung Pay and Google Pay.
“It is important that Apple’s measures do not deny consumers the benefit of new payment technologies, including better choice, quality, innovation and competitive prices,” said Margrethe Vestager, the EU’s Competition Commissioner and Executive Vice President.
The commissioner added that she had not set a deadline for the investigations to be completed.