"Paris 2024 gives its full support to Thomas Jolly as well as the creators and artists of the opening ceremony in light of the attacks against them," a spokesperson told AFP.
French investigators have opened an inquiry after Jolly, who is openly gay, complained of cyberbullying following the performance, sources close to the case said Friday.
The open-air ceremony along the River Seine last Friday has drawn praise despite being complicated by an unexpected downpour.
But Christians and far-right groups have taken offence at one of its scenes including members of the LGBT community that they say mocks Christian values, a claim the theatre director has rejected.
Jolly filed a legal complaint on Tuesday, "explaining he had been targeted on social media by threatening and insulting messages criticising his sexual orientation and wrongly assumed Israeli origins", the Paris prosecutor's office said.
They were notably investigating death threats against him, it added.
A source close to the case said many of the hate messages had been in English.
Jolly and his colleagues did not immediately respond to a request for comment.
Investigators are also looking into similar complaints from Barbara Butch, a French DJ and lesbian activist who starred in the controversial scene.
Her lawyer said she had been "threatened with death, torture and rape".
Ceremony organisers have said they were portraying feasting Olympian gods in a nod to a host of famous classical paintings, with a blue-painted French pop star and actor, Philippe Katerine, playing Dionysus, the father of Sequana, the goddess of the River Seine.
But critics have wrongly seen it as a disrespectful parody of the Last Supper, the final meal between Jesus and his apostles.
Former US president Donald Trump, who is seeking re-election to the White House in November, called the ceremony a "disgrace".
Turkey's President Recep Tayyip Erdogan, who hails from an Islamic-rooted party, condemned it for "immorality against all Christians".
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