Pillay's comments came as Iran's police chief warned that anti-government protesters could expect harsh treatment if they took part in further banned rallies.
"People have a right to express their feelings and to hold peaceful protests without being beaten, clubbed and thrown into jail," Pillay said in a statement issued from her Geneva office.
"I am shocked by the upsurge in deaths, injuries and arrests. The government has a duty to ensure that the violence does not escalate," the statement said.
While noting that it was not yet clear how eight people died when protests were suppressed in Iran last Sunday, she said information available "suggests excessive acts of violence by security forces and the para-military Basij militia".
She reminded Tehran that it was a signatory to the U.N.'s International Covenant on Civil and Political Rights which bars arbitrary arrest and declares that the right to freedom of expression and peaceful gatherings are universal.
High Commissioner for Human Rights since 2008, Pillay has shown mounting readiness to speak out against what she sees as abuses in U.N. developing country members who are generally shielded from criticism in the 47-nation Human Rights Council.
Pillay, formerly defence attorney for opponents of apartheid in South Africa and more recently a judge at the International Criminal Court at The Hague, also voiced alarm at arrests of opposition activists, journalists and human rights defenders.
(Editing by Louise Ireland)
