Attal, a former education minister, said the state would be filing a complaint against the student over falsely accusing the headmaster of mistreatment during the incident in late February.
"The state... will always stand with these officials, those who are on the frontline faced with these breaches of secularism, these attempts of Islamist entryism in our education establishments," he said during the evening news on the TF1 television channel.
Secularism and religion are hot-button issues in France, which is home to Europe's largest Muslim community.
In 2004, authorities banned school children from wearing "signs or outfits by which students ostensibly show a religious affiliation" such as headscarves, turbans or kippas on the basis of the country's secular laws which are meant to guarantee neutrality in state institutions.
The government last year said it was also banning the abaya -- a garment worn by Muslim women that covers the body from the neck to the feet -- in schools.
The headmaster's departure comes amid deep tensions in the country following a series of incidents including the killing of a teacher by an Islamist former pupil last year.
Early retirement
The principal at the Maurice-Ravel lycee in eastern Paris quit after receiving death threats online following an altercation with a student last month, officials told AFP on Tuesday.
On February 28, he had asked three students to remove their Islamic headscarves on school premises, but one of them -- an adult who was at the school for vocational training -- refused and an altercation ensued, according to prosecutors. The principal later received death threats online.
In a message addressed to the school's staff, quoted by French communist daily L'Humanite, the principal said that he had taken the decision to leave for his "safety and that of the school".
Education officials said he had taken "early retirement".
Attal told TF1 the headmaster had been supposed to retire in June, and decided to leave a little earlier.
The student had lodged a complaint against the principal, accusing him of mistreating her during the incident.
She told French daily Le Parisien that she had been "hit hard on the arm" by the headmaster.
But the Paris prosecutor's office on Wednesday told AFP that her complaint had been dismissed.
An investigation has been opened into cyber-harassment following the death threats against the headmaster.
A 'collective failure'
Politicians from across the spectrum on Wednesday said they were shocked by the resignation.
"It's a disgrace," Bruno Retailleau, the head of the right-wing Republicans faction in the Senate upper house, said on X (former Twitter).
Boris Vallaud, the head of the Socialist deputies in the National Assembly lower house, told television broadcaster France 2 the incident was "a collective failure".
Marion Marechal, the granddaughter of far-right patriarch Jean-Marie Le Pen and a far-right politician herself, spoke on Sud Radio of a "defeat of the state" in the face of "the Islamist gangrene".
Maud Bregeon, a lawmaker with President Emmanuel Macron's Renaissance party, also took aim at "an Islamist movement".
"Authority lies with school heads and teachers, and we have a duty to support this educational community," Bregeon said.
Socialist Paris mayor Anne Hidalgo called the principal to "assure him of her total support and solidarity", said her office, adding she was "appalled and dismayed".
Bomb threats
The education ministry earlier said that the principal's decision to leave his post was "understandable given the seriousness of the attacks against him".
Education Minister Nicole Belloubet had visited the school in early March and deplored the "unacceptable attacks".
A 26-year-old man has been arrested for making death threats against the principal on the internet. He is due to stand trial in April.
The uproar comes as dozens of French schools have received attack threats in recent weeks.
Attal has pledged to "hunt down" the people responsible for sending them.
Around 50 schools in Paris received new bomb threats on Wednesday, some including a "very violent video", education authorities said. The mayor's office said classes were briefly interrupted for security checks.
The prime minister pledged to increase security, including near schools, after the Islamic State jihadist group claimed responsibility for the killing of 137 people at a Moscow concert on Friday.
