Nikki Haley also said the worldwide community can't let Iran silence protesters' messages, particularly by blocking some social media platforms.
The U.S. called the meeting after giving moral support to the anti-government protesters in a week of demonstrations and counterdemonstrations.
Russian Federation portrayed the Security Council meeting as a US attempt to violate Iran's sovereignty.
At least 21 people have been killed amid the anti-government protests and unrest over the country's economic woes - demonstrations Iran has accused the US of stirring up.
At Friday rallies in Iran, pro-government demonstrators chanted "Death to America" and "Death to Israel". A similar rally followed Friday prayers in Tehran.
Hundreds carried out demonstrations in front of the Brandenburg Gate in Germany in support of Iranian protesters facing repression from the government in the past two weeks.
Haley said Friday that "the world should applaud their courage", and the USA "stands unapologetically with those in Iran who seek freedom for themselves".
Iran's state TV on Saturday showed government supporters rallying a day after the foreign minister said a USA move to call an emergency U.N. Security Council meeting to discuss anti-government protests was another Trump administration "blunder".
"The Iranian people are rising up in over 79 locations throughout the country", Haley told the council.
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Haley went on to destroy the Iranian regime, denouncing their involvement in the Syrian civil war and supporting Syrian President Bashar al-Assad.
Iran is not a member of the Security Council but its ambassador, Gholamali Khoshroo, was invited to participate. "Let Iran deal with its own problems".
The widespread demonstrations were initially triggered by the worsening economic situation in the country but soon touched upon other issues relevant to the level of democracy and respect for human rights in the country.
"Why is the United States, a permanent member of the Security Council and one of the authors of the UN Charter, undermining the authority of the Security Council as the main body responsible for maintaining worldwide peace and security?"
The French diplomat was blunt when he said that the violations of the demonstrators' rights "do not constitute per se a threat to global peace and security".
Lawmaker Mahmoud Sadeghi said that around 90 university students 58 of them in the capital Tehran have been detained since protests broke out, the semi-official ILNA news agency reported Saturday.
"However worrying the recent events were, they did not constitute a threat to global peace and security".
But France's ambassador, Francois Delattre, urged caution, saying the council should act "with all the vigilance required, guarding against any exploitation of this crisis, which would only reinforce the extremes".
"It's another attempt [at bullying] by the US, which has lost authority and credibility in the eyes of the whole world", said Khoshroo.