It comes after Russian Federation vetoed a rival resolution that blamed Iran for fueling the conflict there.
US Ambassador to the UN Nikki Haley slammed the Russian veto.
Russia's ambassador to the UN, Vassily Nebenzia, said the wording in the British draft would have had "destabilising ramifications" if adopted, and warned about the effect it would have on Yemen and the region as a whole. It would also expand sanctions criteria to include "any activity related to the use of ballistic missiles in Yemen".
Iran's mission to the United Nations charged that the United States and Britain had pushed an "unwarranted draft resolution" to advance an anti-Iran political agenda.
"We can not concur with uncorroborated conclusions and evidence which requires verification and discussions within the sanctions committee", Russian Ambassador Vassily Nebenzia told the council.
Immediately after the resolution was vetoed, the council unanimously passed a resolution drafted by Russian Federation to extend the arms embargo on the Yemeni rebels for another year.
"If Russia is going to use its veto to block action against Iran's risky and destabilizing conduct, then the United States and our partners will need to take actions against Iran that the Russians can not block", Haley claimed.
Washington has charged Iran with supplying Yemen's Houthi rebels with arms including surface-to-surface missiles that have been used against countries supporting a Saudi-backed offensive against the militants.
Diplomats said Russian Federation could veto the British text, allowing for a vote on its own draft resolution.
Punjab CM's son-in-law booked in Rs 97-cr OBC loan default case
The loan amount was then converted into a non-performing asset on March 31, 2015. It was later declared by the bank as an alleged fraud of Rs. 97.85 crore.
Meanwhile, Iran's envoy to the United Nations says that the U.S. and the UK are trying to distract the global community away from Saudi Arabia's war crimes in Yemen by drafting such resolutions.
The British-drafted resolution called to condemn Iran for violating a United Nations arms embargo by providing missiles and drones to Shiite rebels in Yemen, as well as to take future action against Tehran.
Illustrative image of tribesmen loyal to Houthi rebels chanting slogans during a gathering aimed at mobilizing more fighters into battlefronts to fight pro-government forces, in Sana'a, Yemen, January 3, 2017.
After the UNSC failed to pass the UK-drafted resolution, Russian Federation proposed its own draft later on Monday, which was subsequently and unequivocally adopted by the UNSC.
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.
It said Tehran had failed to prevent Houthi rebels from obtaining Iranian missiles, including one fired hundreds of miles into Saudi Arabia.
But the United States has accused Iran of being the aggressor and has pressed the UN council repeatedly to take action to punish Tehran. The embargo was due to expire at midnight on February 26.
No mention of this by United Kingdom at #UNSC & in resolution?