According to a report by London-based daily, Al Quds Al-Arabi, Abdullah al-Hamid described Nayef as a "US mercenary", and asked for trying the Saudi prince for such crimes as fabrication of realities, autocracy, involvement in terror and assassination attempts.
He stressed that the Saudi interior minister should be prosecuted by the law and should be sacked from his post for involvement in torture and violation of human rights.
Hamid also asked for the immediate freedom of political prisoners from Saudi jails.
In similar remarks this month, Executive Director and Founder of the Center for Democracy and Human Rights in Saudi Arabia Ali Al-Yami called newly-appointed Interior minister a "cruel man", saying he spares no hostile measure to serve the al-Saud regime.
"Mohammed bin Nayef is notorious for cruelty and he spares no brutal action to serve the al-Saud regime," Al-Yami told Iran's Arabic-language news network Al-Alam.
Saudi Arabia has faced demonstrations on an almost regular basis in Eastern Province, mainly in Qatif and the town of Awamiyah since February 2011, calling for the release of all political prisoners, freedom of expression and assembly, and an end to widespread discrimination.
However, the demonstrations have turned into protests against the repressive Al Saud regime, especially since November 2011, when Saudi security forces killed five protesters and injured many others in the province.
Saudi forces have also arrested dozens of people including prominent Shiite cleric Sheikh Nemr al-Nemr.
According to Human Rights Watch, the Saudi regime "routinely represses expression critical of the government."
Last month, the Saudi Interior Ministry warned the public against staging demonstrations in support of the prisoners in the kingdom and pledged to deal "firmly" with those participating in such protest rallies.