Mahsa Amini, 22, from Iran's western Kurdistan province, fell into a coma after being detained in Tehran last week for violating the strict dress code for women, under which they must cover their hair.
Her death was announced on September 17, leading to protests across the country. Rights groups on Friday reported at least 36 people had been killed in the authorities' response to the demonstrations.
“I contacted her family at the very first opportunity and I assured them we would continue steadfastly to investigate that incident,” Mr Raisi said in New York on the sidelines of the UN General Assembly.
“Our utmost preoccupation is the safeguarding of the rights of every citizen.”
Mr Raisi said the responsibility now lay in the hands of the judiciary and that the authorities were doing everything needed.
Seeking to turn the tables on Washington, the Iranian president asked: “What about all the people killed by American police? Did all these deaths get investigated?”
He criticised the “double standards” in the West over human rights and said “bad things” happen to people at the hands of authorities everywhere.
Mr Raisi's comments came as the US special envoy for Iran, Robert Malley, expressed support for Iranian women in their protests against the government.
“As President Biden said yesterday at the UN, the United States supports the brave women in Iran peacefully demonstrating to secure their basic rights and condemns the government’s brutal repression,” Mr Malley said on Twitter.
Iran's army warned on Friday that it would “confront the enemies” to ensure security and peace in the country, saying: “These desperate actions are part of the evil strategy of the enemy to weaken the Islamic regime.”
Demonstrators, mostly women, set fire to police stations and vehicles during protests in several Iranian cities as the government shut off the internet in parts of Tehran and the Kurdistan region.
Videos circulated on social media showing women burning their headscarves and cutting their hair while dancing around fires on the streets.
Security forces were seen firing teargas and water cannon to disperse protesters as they chanted “death to the dictator”.
Amnesty International reported that officers fired birdshot and beat protesters with batons.
“On the 7th day of #IranProtest, officials admit to at least 17 deaths w/ independent sources say 36,” the New York-based Centre for Human Rights in Iran said on Twitter late on Thursday.
Access to social media platforms such as Instagram and WhatsApp was blocked as authorities tried to contain the protest movement.
The scope of the unrest remains unclear, but the protests appear to be the most widespread since demonstrations caused by price increases in late 2019.