The UN rights office is pressing Egyptian authorities to allow it to deploy monitors in the crisis-wracked country.
Spokeswoman Liz Throssell told reporters on Tuesday that the office was seeking a green light to send "several" human rights observers to assess the situation.
"We're calling to have human-rights officers allowed on the ground in Egypt so they can gather information, they can talk to NGOs, national human-rights institutions, draw up reports," she added.
Last Thursday, UN rights chief Navi Pillay demanded an "independent, impartial and credible" probe into the bloody crackdown by Egypt's security forces, saying anyone found guilty of wrongdoing should be held to account.
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According to Egyptian authorities, hundreds of people were killed in last Wednesday's assaults on two Cairo protest camps of supporters of ousted President Mohamed Morsi, in the country's worst violence in decades.
The Muslim Brotherhood has put the death toll at over 2,000, while government figures have said at least 830 people have died nationwide.
Throssell said that Egypt's UN ambassador had held talks with senior human rights officials in Geneva the day Pillay made her appeal, and had informed them that a probe had been launched.
Since then, the UN has also called for an investigation into the deaths of three dozen Islamist detainees in police custody, and condemned an armed ambush of police buses in Egypt's Sinai Peninsula on Monday that left 25 policemen dead.
With hundreds of Muslim Brotherhood members, including senior leaders, caught up in the security forces' dragnet, Throssell also said Egypt's treatment of detainees was under watch.
"Everyone deprived of liberty must be treated humanely and afforded all judicial guarantees under international law," she said.
A day earlier, Ban Ki-moon, the UN secretary-general, called for a "full investigation" into the deaths of the 37 prisoners, while the US voiced deep concern over the deaths.
Martin Nesirky, Ban’s spokesman, said the UN chief was "deeply disturbed by the reported deaths" of the prisoners as they were being transferred to a different facility in Cairo.
"He calls for a full investigation to ascertain the facts surrounding this incident," Nesirky said.
Authorities said the detainees died after police fired tear gas on Sunday night in a bid to free an officer taken hostage by prisoners, as the inmates were being transferred to Abu Zaabal prison near Cairo.
But the Anti-Coup Alliance, which includes the Muslim Brotherhood, held the police accountable, accusing them of "murder".
The Alliance has demanded a formal investigation into the deaths, for which divergent explanations have been given.
Photos provided by the lawyers representing the detainees show dead bodies with charred faces and limbs and others covered in bruises which the lawyers said were signs of torture.
The US State Department termed the deaths "suspicious".
"We are ... deeply troubled by the suspicious deaths of Muslim Brotherhood prisoners in a purported prison escape attempt near Cairo," State Department spokeswoman Jen Psaki told reporters.
Source: Al Jazeera and agencies