The human rights organization says Judge Ebrahim Raisi should be investigated for his part in the 1988 mass killings of political prisoners in Iran.
Amnesty International has called for the new Iranian president-elect to be investigated for alleged crimes against humanity.
Long-serving judge Ebrahim Raisi won more than 60% on the vote on Friday, seeing off his pre-selected rivals in an election marked by historic low turnout.
The hardline current Chief Justice of Iran is set to be inaugurated in August, taking over from the more moderate outgoing administration of Hasan Rouhani.
But Agnes Callamard, Amnesty International's secretary-general and formerly the United Nations' special rapporteur on extrajudicial executions, has called for Raisi to instead be investigated for the “crimes against humanity of murder, enforced disappearance and torture”.
New Iranian premier's involvement in 1988 massacre
In 1988, nine years after the Islamic Revolution that saw in Iran's current theocratic political system, Raisi was serving as a deputy prosecutor in the capital, Tehran.
He and three other officials were selected by the country's then-leader, Ayatollah Khomeini, to sit on an entity known as the Tehran 'death panel' or 'death commission'.
Khomeini had ordered the mass execution of leftists and resistance groups being held in prisons across Iran after the end of the Iran-Iraq war. In late July 1988, 'death commissions' were formed across the country to decide prisoners' fates based on their political allegiances.
More than 2,800 people were hanged and shot by firing squad across Iran in the first fortnight, including 750 to 950 in Tehran's prisons of Evin and Gohardasht.
A second, unquantified wave of killings then took place that September, this time based on the remaining prisoners' adherence or non-adherence to Islam.
The executed prisoners' bodies were buried by night in mass graves and their location has not been revealed to families in the decades since.
Callamard said on Saturday: "That Ebrahim Raisi has risen to the presidency instead of being investigated for the crimes against humanity of murder, enforced disappearance and torture, is a grim reminder that impunity reigns supreme in Iran."
"The circumstances surrounding the fate of the victims and the whereabouts of their bodies are, to this day, systematically concealed by the authorities, amounting to ongoing crimes against humanity."
Long-serving justice denies criminal liability
Raisi is sanctioned by the United States for his part in the 1988 killings. He is also sanctioned by the European Union over human rights violations.
He has accepted that he sat on the Tehran panel, but denied having a major role in the decisions it took.
Raisi later went on to hold a series of senior posts in the Iranian judiciary, which is also responsible for the country's prison system, rising to the rank of Chief Justice in March 2019.
During his decades-long career, Amnesty also accused Raisi of presiding over a “spiralling crackdown” on human rights. In recent years the Iranian judiciary has failed to prosecute security forces for the killing, detention and torture of civilian protesters in November 2019.
If Raisi travels abroad as president he could potentially be investigated by a foreign state under the principle of universal jurisdiction, which allows for certain types of international crimes to be enforced against anywhere in the world.
“We continue to call for Raisi to be investigated for his involvement in past and ongoing crimes under international law, including by states that exercise universal jurisdiction," Callamard said.
"It is now more urgent than ever for member states of the UN Human Rights Council to take concrete steps to address the crisis of systematic impunity in Iran."
Amnesty has also called for the UN to hold an independent inquiry into the 1988 killings.