The text, strongly supported by the United States, won 11 favorable votes at the 15-member Security Council but was blocked by Russia's veto.
China and Kazakhstan abstained, while Bolivia also voted against the measure. Nine votes and no vetoes from the five permanent council members -- Britain, France, China, Russia and the United States -- are required to adopt resolutions at the Security Council.
After the veto, the council unanimously adopted a Russian-drafted measure that extended for one year the sanctions regime against Yemen, but that text made no mention of Iran.
The report by a UN panel of experts in January concluded that Iran was in violation after determining that missiles fired by the Huthis at Saudi Arabia last year were made in Iran.
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After hours of negotiations to try to reach a compromise, Russia made clear it had strong reservations about the findings of the report and would not support a draft resolution that mentioned them.
"We cannot concur with uncorroborated conclusions and evidence which requires verification and discussions within the sanctions committee," Russian Ambassador Vassily Nebenzia told the council.
After the Russian veto, US Ambassador Nikki Haley released a statement accusing Russia of protecting "the terrorist-sponsoring regime in Iran" and warned of further action targeting Iran.
"If Russia is going to use its veto to block action against Iran's dangerous and destabilizing conduct, then the United States and our partners will need to take actions against Iran that the Russians cannot block," said Haley, who was traveling to Honduras.
A Saudi-led coalition supporting Yemen's government has been fighting the Huthis since 2015 in a war that has led to what the United Nations describes as the world's worst humanitarian crisis.