Egyptian authorities have been accused of using abductions, torture and other shocking tactics as a tool to stifle dissent.
Amnesty International urged the Egyptian president to acknowledge and investigate serious human rights violations.
But Egypt's Foreign Ministry hit back at Amnesty, saying the group was "biased" and that it seeks to "tarnish Egypt's image".
The exchange came as Amnesty released a new report that says there has been an "unprecedented spike" in enforced disappearances since early 2015 in Egypt under the pretext of fighting terrorism.
International human rights law defines enforced disappearance as the secret abduction or imprisonment of a person, followed by the state's refusal to acknowledge that person's fate.
Amnesty's report entitled Egypt: 'Officially, You Do Not Exist documents 17 cases that the London-based group says reveal "the shocking and ruthless tactics" of the Egyptian authorities to crack down on government opponents. Rape, electric shocks and arrests of other family members were also used to force victims to give false confessions, it said.
Victims range from political activists to children as young as 14, the group said, adding that its report is based on more than 70 interviews with lawyers, non-government organisations, released detainees and family members of victims of torture and enforced disappearance.
Philip Luther, director of the Middle East and North Africa Programme at Amnesty International, said that "the report exposes not only the brutality faced by those disappeared but also the collusion between national security forces and judicial authorities, who have been prepared to lie to cover their tracks or failed to investigate torture allegations, making them complicit in serious human rights violations".
Egypt's Foreign Ministry rejected the report, saying in a statement that Amnesty is "biased, politicised and has special interest in tarnishing Egypt's image". The ministry also said that the group depends on one-sided sources of information and on those who are in a state of "animosity toward the Egyptian state".
Mr Luther noted that Egyptian authorities "have repeatedly denied that enforced disappearances exist in the country".
After abductions, security authorities use torture to extract confessions, in sessions that last up to seven hours, Amnesty said. The report refers to a case of a 14-year-old boy whose name is provided by Amnesty, describing it as one of the most shocking cases of torture. It recounted the repeated rape and abuse of the teenager, which Amnesty said was intended to extract confessions.
The boy was among five children whose cases Amnesty documented in the report.
Mr Luther urged Egyptian president Abdel Fattah el-Sissi to "order all state security agencies to stop enforced disappearances, torture and other forms of ill-treatment and make clear that anyone who orders, commits or is complicit in such violations will be brought to justice".
Police abuses were among the complaints that fuelled the 2011 uprising that ousted autocrat Hosni Mubarak. His elected successor, Islamist Mohammad Morsi, was removed by the military in 2013 after massive protests against Morsi and his Muslim Brotherhood. Then military chief El-Sissi was subsequently elected president in a landslide.
Since Morsi's removal, authorities have cracked down heavily on pro-democracy advocates, as well as Islamist supporters of Morsi.
Egypt's prisons and detention centres are packed with political opponents, and courts have issued heavy prison sentences, often with little evidence or due process. Prosecutors have vigorously applied vague charges such as endangering security or stability, while turning a blind eye to police abuses ranging from torture and forced disappearances to long detentions without charge.
Official records put the number of arrests at over 30,000 from 2013 to 2015. Hundreds more are held facing the death sentence, including Morsi, his supporters and leaders of the Brotherhood, which Mr El-Sissi's government has declared a terrorist organisation.
Some rights groups estimate that as many as 60,000 people have been detained for political reasons in Egypt since July 2013, according to Amnesty.