PARIS—Google Inc. is appealing a French data-protection order to expand Europe's right to be forgotten to its websites world-wide, kicking off a legal tussle over the territorial scope of a rule established last year by the European Union's top court.

The Mountain View, Calif., company said Thursday it sent a request to France's Commission Nationale de l'Informatique et des Liberté s, or CNIL, asking it to rescind a May orderâ "disclosed publicly in June that would force Google to apply Europe's right to be forgotten to "all domain names" of the search engine, including google.com, not just Google sites aimed at Europe, like google.co.uk.

Established just over a year ago by the EU's Court of Justice, the right to be forgotten gives European residents the ability to demand that search engines remove links that appear in searches for an individual's name. Google has so far removed more than 1 million links under the ruling but has insisted on only doing so for its EU websites.

"We believe that no one country should have the authority to control what content someone in a second country can access," Peter Fleischer, Google's global privacy counsel, wrote in a statement provided by a spokesman Thursday. "We respectfully disagree with the CNIL's assertion of global authority on this issue."

The CNIL and some other European regulators have assailed the company's strategy, arguing the ruling says nothing about applying only to European domain names. They say Google's approach makes it easy to find private information that individuals had wanted removed by searching its non-European sites.

The CNIL indicated Thursday that it is prepared to defend its order. "There is no effectiveness if the right is applied only in Europe," a CNIL spokeswoman said.

The CNIL had initially given Google 15 days to comply with the order but had later extended the deadline to the end of the month. If Google doesn't comply, the CNIL can open sanctions proceedings that could lead to a fine of up to €150,000.

Write to Sam Schechner at sam.schechner@wsj.com

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