The ultra-conservative president vowed to "act decisively" against the protesters in a phone call with relatives of a security forces man killed in the protests.
Raisi has recently returned to Iran from the United Nations General Assembly in the United States.
- We have made it clear many times that if someone has a reasonable point of view, we will listen to it.
But anarchy?
To disturb the national security, the security of the people?
No one will give in to this, says the president further.
Triggered by death in custody
The demonstrations began when a 22-year-old woman arrested by the Islamic dictatorship's hardline morality police died in custody.
She was suspected of breaking the strict rules on headwear for women.
Those rules have been tightened since the particularly conservative Ebrahim Raisi came to power last year.
22-year-old Mahsa Amini is said to have been hit in the head with a baton and had her head slammed against a vehicle.
Police claim she suffered some sort of sudden heart problem and Interior Minister Ahmad Vahidi also insists the young woman was not subjected to any violence.
- Reports from the supervisory bodies have been received, witnesses have been interviewed, films have been reviewed, forensic reports have been produced and it turns out that there had been no abuse, says Vahidi according to the British BBC.
Sharp shots
The protests have spread to most of Iran's 31 provinces and in many cases degenerated into clashes between disgruntled citizens and security forces.
According to the authoritarian state's official figures, 41 people have been killed so far, but independent actors claim that there are even more.
Just last Wednesday night, 19 civilians were shot dead by the security forces, according to the human rights organization Amnesty International.
Three of those killed are said to have been children.
Photos and videos shared by various rights organizations appear to show security forces firing into crowds.
Hundreds, probably thousands, of people have been arrested in connection with the protests.
The authorities have also shut down large parts of the internet in several places.
Alongside that, demonstrations have also been organized in support of the authorities and the strict rules on women's headscarves.
Her death sparked a wave of protests in Iran:
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Protests after Mahsa Amini's death - this has happened.
Photo: KENZO TRIBOUILLARD/AFP/TT