LUXEMBOURG — Google is pushing back against France’s data privacy authority after the watchdog ordered the search engine giant to extend the so-called right to be forgotten to its websites globally.

France’s data protection authority CNIL should withdraw an ultimatum threatening Google with fines unless it delists requested links across its network, the California-based company said in a blog post Thursday.

“We respectfully disagree with the CNIL’s assertion of global authority on this issue,” Peter Fleischer, Google’s global privacy counsel, said in the post. The French regulator’s order from last month “is a troubling development that risks serious chilling effects on the Web,” he said.

The order comes just over a year after a judgment by the EU’s highest court created a right to be forgotten – allowing people to seek the deletion of links on search engines if the information was outdated or irrelevant. The ruling led to a furor, with Google appointing a special panel to advise it on implementing the law. The panel opposed applying the ruling beyond EU domains.

Failure to comply could lead to sanctions, Isabelle Falque- Pierrotin, the president of CNIL, said in June. She currently also heads the group of EU data protection commissioners who urged Google to remove links, when needed, from .com sites and not just from European sites.

The right-to-be-forgotten rules add to a growing list of challenges the company is facing in Europe.

EU antitrust regulators in April escalated their 4-year probe. In a statement of objections they accused the Internet giant of abusing its dominance of the search-engine market and started a new investigation into Google’s Android mobile-phone software.