"Think of us", she said.
A total of 21 people died and hundreds were arrested in five days of unrest that began on December 28, 2017.
Mass pro-government rallies have taken their place in many Iranian cities.
Foreign Minister Mohammad Javad Zarif wrote on Twitter after the session that the Security Council "rebuffed the U.S.' naked attempt to hijack its mandate".
Haley said that "in the end, the Iranian people will determine their own destiny", and she reiterated U.S. support for the protesters.
Bolivian ambassador Sacha Sergio Llorenty said: "It needs to be crystal clear to the worldwide community that the situation in Iran does not belong on the agenda of the Security Council".
United Nations 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 United Nations agency for human rights.
'There are workers who say they have not received their salaries for months.
The regulator, known as Ofcom, said Friday the letter is being carefully evaluated.
A traditional drama in the best sense of the word
Indeed, Ellsberg was prosecuted under the Espionage Act and faced the possibility of a 115-year sentence. I was reading the Los Angeles Times because my wife and I were there last month to visit our daughters.
The U.S. called on Tuesday for such a session, but council members could insist on a vote before taking up the topic, and it would take nine of the 15 votes to go forward.
Ofcom has a broad regulatory role in Britain, overseeing television, radio, high-speed internet and other sectors.
"The Iranian regime is now on notice: The world will be watching what you do", Ms Haley said.
The Islamic State group has declared support for the anti-government protests in Iran. He added that President Rouhani, and the ruling Iranian regime as a whole, are incapable of employing moderate policies. The protests are the most widespread of their kind in Iran since the unrest that followed 2009's disputed presidential election.
The meeting began as a closed-door session but the United States was able to ensure a second, open phase of talks thereafter, despite resistance from Russia, France, Bolivia and other members.
"We have hard evidence of the violence in Iran by a handful of protesters, in some cases resulting in the deaths of policemen and security officers, being very clearly directed from overseas".
They said they are also very concerned about reported shutdowns of social media services such as Instagram and messaging services like Telegram, arguing that "communication blackouts constitute a serious violation of fundamental rights".
In Tehran, a hard-line cleric leading Friday prayers expanded the blame to include popular worldwide messaging apps, calling on the Islamic Republic to build its own social media. The people have lost trust in the leadership of the country, with corruption and increasing inequality ripping about the social construct of the country, and contributing to mass injustice among its people.
Russian Ambassador Vassily Nebenzia said the United States is abusing the Security Council's platform. "In the spirit of frankness and respect that is at the basis of our relationship, we expect all concerned to refrain from violence and the right of expression to be guaranteed, also in light of the statements made by the Iranian Government". Large pro-government rallies were held in response, and officials have blamed the anti-government unrest on foreign meddling. It marked the third day of such demonstrations. Iran's other media outlets did not report on protests.
U.S. president Donald Trump has been the most vocal supporter of Iran's anti-government protesters. Government supporters turned out in force in Tehran and elsewhere on Friday.