The UN rights office said it was deeply concerned by "the seriously damaging lack of accountability for human rights violations committed by security forces in the context of demonstrations".
Spokesman Rupert Colville said at least five people, including two security officers, had been reported killed in clashes during protests at the weekend.
Islamists have been protesting the military's overthrow of president Mohamed Morsi last year and also the dropping of murder charges against former president Hosni Mubarak who was accused of responsibility for the deaths of hundreds during the 2011 uprising that ended his three decades rule.
"The authorities must ensure that security forces do not resort to the excessive use of force," Colville told reporters in Geneva.
"Prompt, thorough and independent investigations" should be carried out "into all human rights violations committed in the context of protests," he added.
He also urged protesters to act peacefully, saying "the increasing polarisation in Egyptian society is very alarming".
Protests by Islamists in Egypt are increasingly turning into armed attacks in response to a security crackdown that has resulted in hundreds of deaths and led to the jailing of thousands.
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The UN rights office also criticised last week's conviction of around 80 students for illegal demonstrations and vandalism in protests backing Morsi.
"We urge the government to immediately release all those who have been detained for legitimate exercise of their rights to peaceful assembly and to freedom of association and expression," Colville said.
He also alluded to Saturday's court decision dropping the Mubarak murder charges.
"We are closely following attempts to bring to justice those responsible for serious human rights violations in Egypt, including the killings of hundreds of people in February 2011," he said.
"We urge the authorities to ensure that all those who are responsible for human rights violations, up to the highest levels, face justice in line with international standards of fair trial and due process," he said.
Also mentioning the government crackdown on Morsi supporters in August 2013, which left hundreds dead, he stressed that "victims and their loved ones have the right to justice and accountability and to reparations and compensation".
"Egyptian authorities have the duty to ensure that perpetrators of serious human rights violations do not enjoy impunity," he said.