PARIS, March 31 (Reuters) - Apple was hit with a 150 million euro ($162.42 million)fine by French antitrust regulators on Monday for abusing its dominant position in mobile app advertising on its devices between 2021 and 2023 thanks to a privacy control tool.

The French competition watchdog however did not order Apple to change the tool.

The fine is the first by any antitrust regulator against Apple over its App Tracking Transparency (ATT).

ATT allows iPhone and iPad users to decide which apps can track user activity but it has been criticised by advertisers and rivals dependant on online advertising.

The French case was triggered by complaints from several associations for online advertisers, publishers and internet networks accusing Apple of allegedly abusing its market power.

"While the objective pursued by ATT is not in itself open to criticism, the way it is implemented is neither necessary nor proportionate to Apple's stated objective of protecting personal data," the regulator said in a statement.

It added that the privacy tool "particularly penalized smaller publishers," as they depend to a large extent on the collection of third-party data to fund their business.

The French watchdog also ordered Apple to publish the decision on its website for seven days.

The fine is much smaller than the 1.8 billion euro penalty meted out by the EU competition enforcer to Apple last year for hindering music streaming rivals via restrictions on its App Store, a case triggered by a complaint from Swedish streaming service Spotify.

Apple said it was disappointed with the French fine but that the regulator had not required any specific changes to its privacy control tool.

Apple's ATT is also in the German antitrust agency's crosshairs which in February charged the company with giving itself preferential treatment.

Monday's decision confirmed a Reuters story from last month.

($1 = 0.9239 euros)