Iran's government also organized two days of mass demonstrations across the country Wednesday and Thursday as a sign of strength and to reassure those worried about the unrest.
It is not precisely clear what Ms Haley hoped to achieve by convening the session, which was not previously scheduled.
Several countries - including U.S. allies France and the United Kingdom - used Friday's Security Council meeting to defend the nuclear agreement between Iran and world powers.
The charge against Rouhani is that he has failed to deliver the good times promised.
"The control and censorship of information through the blocking of internet and messaging services represents an unlawful restriction of the right to freedom of expression and prevents the population from accessing communication and services".
Les Etats-Unis envisagent d'imposer de nouvelles sanctions à l'Iran
Leurs entreprises seraient pénalisées aux Etats-Unis si elles continuaient à commercer avec l'Iran. Cet accord nous engage, comme tous les pays qui l'ont conclu.
Iran's Ambassador Gholamali Khoshroo slammed the meeting as a "farce" and a "waste of time" and said the council should instead focus on addressing the Israeli-Palestinian conflict or the war in Yemen.
The United States has long stood with those who yearn for freedom and a brighter future, and yet the president declined to stand with a proud people who sought to escape from under the heavy weight of a dictatorship, issuing only a delayed response condemning the regime's violence.
Demonstrations erupted in Iran more than a week ago after the government announced plans to raise fuel prices and cut monthly cash handouts to lower-income Iranians.
Some reports put the number of people arrested since 28 December as high as 1,700.
One of the largest was in the capital, Tehran, where people chanted anti-US slogans, blaming Washington for the unrest.
Those protests have petered out in recent days while pro-government rallies have gained momentum.
UN human rights experts urged Iranian authorities to respect the rights of protesters and voiced concern over Tehran's restriction of social messaging services in a joint statement issued yesterday by the UN agency for human rights.
Russia accused the United States of interfering in Iranian affairs as the UN Security Council prepared to hold a meeting at Washington's request on deadly protests in Iran.
Another female activist was caught on tape saying, "You raised your fists and ruined our lives [referring to the 1979 Islamic revolution]". Some protesters have yelled "Death to the dictator" - a reference to Khamenei. This past week's protests began in the working class, in what might be called Iran's "fly-over country". All of Iran's radio and television stations are state-run. He claimed that when the government blocked social media, "the riots stopped". So has the pitched battle over American foreign policy on Iran, which renders Iran's domestic realities as talking points in a conversation that is really about us. The CIA declined to comment. It is expected the session, which was requested by the United States, will begin with a briefing by a UN political official. Not a call for reforms, but a rejection of the ruling order.
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