US Ambassador Nikki Haley warned ahead of the meeting that the demonstrations could escalate into full-blown conflict, drawing a comparison with Syria.
"The world has witnessed the horrors that have taken place in Syria, that began with a murderous regime denying its people's right to peacefully protest," Haley said in a statement late Thursday.
"We must not let that happen in Iran."
A total of 21 people have died and hundreds have been arrested since December 28 as protests over economic woes turned against the regime as a whole, with attacks on government buildings and police stations.
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Russia has criticized the US push for Iran to be discussed at the Security Council and accused Washington of interfering in Iran's domestic affairs after President Donald Trump backed the anti-government protests.
Diplomats said they expected Russia to request a procedural vote at the start of the meeting to decide whether the situation in Iran should be on the council agenda.
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. No vetoes apply.
"It will be telling if any country tries to deny the Security Council from even having this discussion, just as the Iranian regime tries to deny its own people the ability to have their voices heard."
Pro-regime rallies were expected to be held in Tehran after Friday prayers, the third straight day of marches held in support of the government, which has declared that the unrest over.
At the request of the United States, the council will hold an open session from 3:00 pm (2000 GMT) during which UN Assistant Secretary General Taye Brook Serihoun will brief on the recent violence.
Russia's Deputy Foreign Minister Sergei Ryabkov on Thursday warned the United States against "any attempt to interfere in the internal affairs" of Iran.
Russia maintains that the protests do not pose a threat to international peace and security and should not be taken up by the Security Council.
Over the past days, the United States has lobbied hard to win support for the meeting, especially from the six new non- permanent council members, diplomats said.
Equatorial Guinea, Ivory Coast, Kuwait, Peru, Poland and the Netherlands began their stint at the Security Council on January 1.
Iran's UN Ambassador Gholamali Khoshroo on Wednesday sent a letter to the council accusing the United States of meddling in its internal affairs and urging countries to condemn Washington's statements.
Trump has pledged to help Iranians "take back" their government.