UN human rights chief Navi Pillay Friday expressed alarm about reported mass arrests of key members of Egypt's Muslim Brotherhood after the military ousted president Mohamed Morsi, and urged all sides to respect fundamental freedoms.

"There should be no more violence, no arbitrary detention, no illegal acts of retribution," Pillay said in a statement.

"Serious steps should also be taken to halt, and investigate, the appalling -- and at times seemingly organised -- sexual violence targeting women protestors," she added.

Pillay's spokesman Rupert Colville told reporters in Geneva that the basis of the detention of individuals including Morsi and other Muslim Brotherhood figures remained unclear.

"It's very important that the authorities address that issue," Colville said.

Pillay said that international human rights standards -- including freedom of speech and assembly -- must be upheld.

"I urge all parts of Egyptian society to exercise these rights in a peaceful manner, so as to avoid any further loss of life. I also urge a major effort by all political parties, and the authorities, to deter and punish any acts of vengeance," she said.

Pillay said that mass demonstrations by Morsi's supporters and his opponents over recent weeks were a clear sign that Egyptians across the political spectrum want their human rights to be honoured.

"The country has so far failed to seize the opportunity to respond to the aspirations of all its citizens and move towards a truly tolerant and inclusive society, based on human rights norms and the rule of law," she said.

"Egyptians deserve to live in a society run by institutions that ensure their rights are respected. I urge everyone to seize this new opportunity to fulfil the country's potential to become a fully functioning and prosperous democracy, without further destabilising upheavals," she added.

Islamist Morsi became Egypt's first democratically elected president in June 2012, after strongman Hosni Mubarak was driven from power, but was himself deposed on Wednesday after mass protests.

His supporters accuse the military of a brazen coup.

Pillay's office refrained from calling for Morsi's reinstatement or labelling his ouster a coup.

"It's very, very complex," said Colville.

"We're calling clearly for a very quick return to the proper democratic process," he said, adding it was clear that the Muslim Brotherhood must remain part of Egypt's future political landscape.