"The coward assassination of General Soleimani, the anti-terrorism hero of our region, was an arbitrary killing & a clear violation of the UN charter," Mousavi wrote on his Twitter account on Thursday.
"The US is responsible for this criminal act, & can’t whitewash this by chastizing the UN. We’ll never forget, we’ll never forgive," the Iranian foreign ministry spokesman added.
Mousavi's remarks came after the 44th session of the UN Human Rights Council in Geneva on Thursday condemned the arbitrary actions of governments, including the assassination of General Soleimani, commander of the Quds Force of the Islamic Revolution Guards Corps (IRGC).
Lieutenant General Soleimani was assassinated in a US drone strike on Baghdad International Airport in Iraq on January 3.
The airstrike also martyred Deputy Commander of Iraq's Popular Mobilization Forces (PMF) Abu Mahdi al-Muhandis. The two were martyred in an American airstrike that targeted their vehicle on the road to the airport.
Five Iranian and five Iraqi military men were martyred by the missiles fired by the US drone at Baghdad International Airport.
Iran announced in late June that it had issued arrest warrants for 36 officials of the US and other countries who have been involved in the assassination of the martyred General Soleimani.
"36 individuals who have been involved or ordered the assassination of Hajj Qassem, including the political and military officials of the US and other governments, have been identified and arrest warrants have been issued for them by the judiciary officials and red alerts have also been issued for them via the Interpol," Prosecutor-General of Tehran Ali Alqasi Mehr said.
He said that the prosecuted individuals are accused of murder and terrorist action, adding that US President Donald Trump stands at the top of the list and will be prosecuted as soon as he stands down presidency after his term ends.