Iran said Tuesday that the vetoing of a U.N. resolution that would have criticized its role in Yemen represented another setback for the United States.
The organisers say they hope to repeat the initiative elsewhere in the capital and in other areas of the country soon.
Iran lashed out at the United States and the United Kingdom for covering war crimes committed by Saudi-led coalition in Yemen.
The initial draft text - to renew the annual mandate of a targeted sanctions regime related to Yemen - wanted to include a condemnation of Iran for violating an arms embargo on Houthi leaders and include a council commitment to take action over it. "In spite of a mountain of credible, independent evidence showing Iran violated the Yemen arms embargo, resulting in a series of attacks on civilian targets, Russian Federation prevented accountability and endangered the entire region".
The statement by Western powers condemning Iran on February 27 shows the United States has galvanized the support of major European allies, all of whom signed Iran's 2015 nuclear deal along with Russian Federation and China, for taking action to deter Iran's ballistic-missile activities.
The latest British draft dropped the condemnation and instead expressed concern that United Nations experts monitoring the sanctions reported Iran had violated a targeted arms embargo by failing to stop missiles and unmanned aerial vehicles reaching the Houthis.
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Amid a dispute between the government and the Houthis over who should receive public sector salaries and as the local currency has shed much of its value, many employees - including some medical staff - have not received wages in over a year.
United Nations statistics show more than 10,000 people, majority civilians, have been killed since the coalition intervened in the Yemeni civil war that also displaced around 3 million.
The four countries also called on all parties involved to comply with global humanitarian and human rights law, to continue allowing humanitarian aid to enter, and to return to peace talks.
U.S. Ambassador to the UN Nikki Haley.
All four countries are signatories to the Iran nuclear deal.