State Department spokeswoman Heather Nauert had suggested the USA government could impose sanctions against Iranian officials who repress peaceful protests.
Iran has witnessed rallies in the past few days over price hikes and economic woes in some cities, but some suspicious rioters, who have been accused of being foreign-backed, have taken the protest so far by damaging public property and attacking police forces.
Haley said that "in the end, the Iranian people will determine their own destiny", and she reiterated United States support for the protesters.
U.S. Ambassador Nikki Haley spoke Friday after her country called the meeting.
U.S. Ambassador Nikki Haley has praised the anti-government demonstrators as courageous freedom-seekers who need the world's support.
But Russia accuses the United States of interfering in Iran's national affairs and called for closed-door talks just before the council's meeting, scheduled for 3:00 pm (2000 GMT).
Kalın, also told reporters during a news conference in Ankara that while Iranian citizens had the right to hold demonstrations, it was not possible to accept acts that cause casualties and property damage, as the protests have left 21 people dead.
Russia's deputy foreign minister, Sergei Ryabkov, has portrayed the Security Council meeting as an American attempt to violate Iran's sovereignty.
"The Iranian regime is finally on notice: The world will be watching what you do", she said.
Khoshroo also said the United States had abused its power as a permanent member of the Security Council by calling for a meeting to discuss the protests.
The US Ambassador to the United Nations KIkki Haley had sought emergency meetings with UN Security Council and the Human Rights Council over the riots in Iran.
Trump's administration has denied having any hand in the demonstrations, saying they arose completely spontaneously.
Russian Federation warned the United States against intervening in Iran and exploiting the situation there to undermine the agreement on Tehran's nuclear program.
The US has been vocal in its support of the demonstrators and offered harsh condemnation of the Iranian government, including a tweet from President Donald Trump that called the Iranian regime "brutal and corrupt".