Evidence, including testimonies from survivors, indicates that supporters of deposed President Mohamed Morsi tortured individuals from a rival political camp, said Amnesty International.
Anti-Morsi protesters told Amnesty International how they were captured, beaten, subjected to electric shocks or stabbed by individuals loyal to the former President.
Since mass rival rallies began in late June, as of 28 July, eight bodies have arrived at the morgue in Cairo bearing signs of torture. At least five of these were found near areas where pro-Morsi sit-ins were being held.
"Allegations that torture is being carried out by individuals are extremely serious and must be investigated as a matter of urgency," said Hassiba Hadj Sahraoui, Deputy Director for the Middle East and North Africa at Amnesty International.
"The apparent use of torture for reprisal attacks is unacceptable. People should not take the law into their own hands. Political leaders have a responsibility to condemn these criminal acts and call on their supporters to renounce such human rights abuses.
The Egyptian government must not, however, use these crimes, carried out by few, as a pretext to collectively punish all pro-Morsi supporters or use excessive force to disperse their sit-ins."
Mastour Mohamed Sayed, 21, told Amnesty International he and a group of 20 others were attacked by a group of Morsi supporters near the pro-Morsi sit-in at Rabaa al-Adawiya on 5 July.
His assailants wore balaclavas and some were armed with knives or machine guns. Some escaped but Mastour Mohamed Sayed and a few others were captured.
"I felt terrorized by the guns pointed at me... They grabbed me...They called us 'infidels'... .We were then driven to the sit-in... I was dragged on the ground. We were eventually held under a podium... I was beaten with bars, and given electric shocks. I lost consciousness a few times," he told Amnesty International.
While he was detained, Mastour Mohamed Sayed said he believed he heard a woman detainee being sexually assaulted and beaten.
"My hands were tied behind my back, and I was blindfolded, but I could see a bit from underneath the blindfold... I could hear the girl screaming when she was given electric shocks. I could also hear a woman ordering her to take off her clothes. At that stage, I said that this was haram (forbidden), and was hit on the head. I then saw two bearded men go into the room and heard the girl screaming more ... "
Afterwards, Mastour Mohamed Sayed saw blood on the floor of the same room. He said his captors asked why he and other detainees supported General Abdel Fattah al-Sisi.
He was allowed to leave the Rabaa al-Adawiya sit-in the following morning, but his identity card was not returned to him.
Amnesty International has found that the capture and torture of suspected anti-Morsi protesters most frequently occurs during or in the immediate aftermath of violent clashes between the two camps.
Karam Hassan, a 48-year-old resident of Giza, was abducted and taken to an unknown location by armed Muslim Brotherhood protesters on 2 July. It followed clashes between residents of Giza and Muslim Brotherhood protestors in Nahda Square.
His body was discovered by his mother in Zenhom Morgue on 10 July. It was covered in bruises and had burn marks on the chest, back, arms and both legs. He had also been stabbed in the chest and had a fractured skull.
Ahmed El Kelhy, Karam's neighbour, who was with him when he was abducted said that armed Muslim Brotherhood supporters were shooting live rounds at the residents. He pointed at two bullet holes in buildings and a bullet-ridden pick-up truck.
Hassan Sabry, aged 20, said that he was dragged by armed assailants into Oumran Garden, near the pro-Morsi protests at Cairo University .
"They used plastic wires to handcuff me... They started to beat us with sticks all over the body. At least two of us were bleeding," he said. He then watched a bloodied protester have his throat slit and another being stabbed to death.
"They then started to beat me on the head. I fell on the ground and pretended to be dead. I held my breath. They thought I died and held me and threw me to a place with the two bodies of the men killed."
Shehab Eldeen Abdelrazek, 23, a journalist, was also dragged into a tent and beaten with wooden sticks on his head, back and legs in Rabaa Eladaweya Square on 3 July.
The Ministry of Interior said on 30 July that 11 bodies bearing signs of torture have been found since the outbreak of the crisis. A further 10 complaints regarding torture were made by survivors.
The Egyptian campaign group "I am Against Torture" told Amnesty International that it had independently verified that 11 people have died following torture at the hands of Morsi supporters since the beginning the crisis.
"Let's be clear: capturing people because they hold different views and torturing them is a criminal act and those responsible must be held to account," said Hassiba Hadj Sahraoui.
Torture or other ill-treatment at the hands of security forces in Egypt has continued under successive governments. Police and security forces continue to torture or otherwise ill-treat detainees with total impunity.