The statement was deemed to be "non-compliant" with the order in a previous High Court judgment that concluded Samsung's Galaxy tablet did not infringe Apple's designs, in part because its products were "not as cool".
The world's two leading smartphone makers are fighting over patents, both for smartphones and for tablets like Apple's iPad, in courts around the world.
South Korea's Samsung argued that Apple's statement, which made potentially confusing references to German and U.S. court decisions as well as the British ruling, was "inaccurate and misleading".
Judges agreed and said Apple must post the new statement within the next 48 hours, although the U.S. company said it would need two weeks to post the notice.
Judge Robin Jacob told Apple's lawyer, Michael Beloff, he did not believe that it would be difficult to post a new statement on the website.
"I would like to see the head of Apple make an affidavit about why that is such a technical difficulty for the Apple company," the Press Association quoted Jacob as saying. "This is Apple that cannot put something on their own website?".
Apple declined to comment on the ruling.
(Editing by Sonya Hepinstall)
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