Russia, China, the UK, France and Germany - who are all signatories to the Iran nuclear deal - responded by saying that they did not recognize the move given that the USA had withdrawn from the agreement.
In a video conference on the Middle East, he cited the lack of consensus in the UN's highest body on the USA strategy as the main reason.
"Iran trusts that the council members will continue preventing that country from undermining the United Nations, including the Security Council", the mission statement said.
Another said that, with the sound rejection of the U.S. bid by nearly the entire Council, "normally the matter is closed".
The move threatens to torpedo the Iran accord and plunge the Council into crisis, while widening the gulf between the U.S. and nearly every other member on Iran policy.
Iranian Foreign Minister Mohammad Javad Zarif welcomed the announcement on Twitter, saying Pompeo's "lawless bullying leaves USA isolated again".
On August 14, the UNSC resoundingly rejected a United States bid to extend an arms embargo on Iran beyond its expiration in October.
The UN Security Council has blocked a controversial bid by the USA to trigger the "snapback" of all sanctions on Iran lifted under a 2015 nuclear deal.
The chair of the UN Security Council, Dian Triansyah Djani, said Tuesday that he would not take any action on a purported US notification for a "snapback" mechanism on sanctions against Iran.
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Djani told members at the end of the meeting that there is no consensus in the council, and that he is not in a position to take further action. "Thus, the president is not in the position to take further action".
In a statement Tuesday evening, the Iranian mission to the United Nations welcomed the council's rejection of the U.S. move.
"Let me just make it really, really clear: the Trump administration has no fear in standing in limited company on this matter", she added. "I only regret that the other members of this council have lost their way and now find themselves standing in the company of terrorists".
Russia's envoy, Vassily Nebenzia, said he hoped the Trump administration would now drop its request, which he said was "not only illegal, but simply will not lead to achieving the result that was envisaged by the United States". He said Beijing is determination to defend multilateralism, the JCPOA and Mideast peace, "whatever the United States says".
Meanwhile, Iranian President Hassan Rouhani on Tuesday said Tehran could reach an agreement with Washington if the U.S. "apologises" and returns to the 2015 nuclear deal, according to Iranian state TV.
"Today's deliberations in the Security Council showed once more the USA isolation on the JCPOA and Resolution 2231", the statement said.
"Put simply: It is Russian Federation and China that revel in this Council's dysfunction and failure", she said.
Gueguen said the three European parties are willing to work with council members including the other JCPOA participants, Russian Federation and China, "to seek a realistic path forward that could secure the support of the council".
Pompeo said the U.S. had the legal right to "snap back" United Nations sanctions within 30 days, even though Trump had pulled out of the nuclear deal in 2018.