"[The U.S.] continues to pursue a policy of open and implicit interference in the internal affairs of other states - doing it unabashedly, openly, under the slogan of caring for democracy and human rights, directly infringing on the sovereignty of other states", Ryabkov said, according to the Associated Press.
Pointing out that her government is monitoring the internal situation in Iran, Wasllström has reportedly said " the UN Security Council is responsible for issues related to global security and peace, meanwhile there are other ways to deal with the current situation in Iran".
US Ambassador Nikki Haley has warned the demonstrations could escalate into full-blown conflict, drawing a comparison with Syria.
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.
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).
She added: "Freedom and human dignity can not be separated from peace and security". "The Iranian regime's contempt for the rights of its people has been widely documented for many years", said Haley, adding that the United States stood "unapologetically with those in Iran who seek freedom for themselves, prosperity for their families, and dignity for their nation".
Russia, a council member, has close ties with Iran, which isn't.
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For a new agenda item to be discussed at the Security Council, at least nine of the 15 council members must support holding the meeting.
Haley's comments come as the United Nations Security Council met to discuss Iran after the U.S. requested an emergency session amid protests in the country. Russian Federation has been vocal in its opposition to the session, with Deputy Foreign Minister Sergei Ryabkov accusing the USA of infringing on Iran's sovereignty. "They do so shamelessly", Ryabkov was quoted as saying by Interfax news agency.
Discussing the domestic situation of Iran at the council "does not help resolve the domestic issue of Iran", said China's Deputy UN Ambassador Wu Haitao.
"This is a matter of fundamental human rights for the Iranian people, but it is also a matter of global peace and security", said Haley.
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".
Equatorial Guinea, Ivory Coast, Kuwait, Peru, Poland and the Netherlands began their stint at the Security Council on January 1.