The draft was presented by France during informal consultations on behalf of the three European powers - Britain, France and Germany -that have been spearheading nuclear talks with Tehran.
The text is an amended version of a draft that has been under discussion this week by the council's five permanent members - Britain, China, France, Russia and the United States - plus Germany.
The draft “decides that Iran shall suspend all enrichment-related and reprocessing activities, including research and development, to be verified by the IAEA, and suspend the construction of a reactor moderated by heavy water."
The text invokes articles 39 and 40 of Chapter Seven of the UN charter that stipulate "provisional measures" to be taken ahead of imposing tougher steps such as sanctions.
But it also expresses the council's intention in the event of Iran's non-compliance with the enrichment freeze demand "to adopt such further measures under Article 41 of Chapter Seven as may be necessary to ensure compliance."
Article 41 provides for a broad range of economic sanctions but does not authorise the use of force.
The new text also calls on all states "immediately to take steps to prevent the transfer of any items, materials, goods and technology that could contribute to Iran's enrichment-related and reprocessing activities and ballistic missile programs."
It gives Iran up to an as yet undecided date in August to comply with the UN demands.
Iranian nuclear negotiator Ali Larijani has stressed that Tehran will take until August 22 to reply to a Western offer of incentives in exchange for freezing its uranium enrichment program.