At least 21 people were killed and 450 were arrested in the protests, many in clashes with security forces trying to quell the rallies.
The protests, the most powerful challenge to the regime in years, appeared to have fizzled Thursday, after a claim by Revolutionary Guards commander Mohammad Ali Jafari that the unrest was officially over. Mass pro-government rallies have taken their place in many Iranian cities.
"We are very disturbed by the way the authorities have responded to the protests," the four Special Rapporteurs said in their statement, released by the Office of the UN High Commissioner for Human Rights.
"The government's instruction to the Revolutionary Guards to hit hard against the protesters, and the judiciary's threats of harsh punishment, are unacceptable.
"We urge the authorities to exercise restraint and respond proportionately in their efforts to control the protests, to limit the use of force to a strict minimum, and to fully respect the human rights of the protesters, including their rights to life, freedom of expression and peaceful assembly."
The UN experts said they shared the concerns of Iranian civil society groups for those arrested.
"We are also very concerned at reports that the Government has blocked the internet on mobile networks, and that social media services like Instagram and messaging services like Telegram have been shut down in an attempt to quell the protests," they said.
"In some regions, internet access has been blocked altogether. Communication blackouts constitute a serious violation of fundamental rights."
The experts added that the lack of measures to address the underlying causes of the unrest through non-violent means was "disturbing."
The protests began just over a week ago over Iran's stagnant economy and the rising cost of living, and developed into a broader outcry against the government.
The United Nations Security Council will convene a meeting on the situation in Iran at 3 p.m. ET Friday. It is expected the session, which was requested by the United States, will begin with a briefing by a UN political official. Iran could also speak.
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