A text of the proposed resolution was distributed to the 15 council nations on Friday, and John Bolton, the US ambassador to the UN, said that a vote could be held early next week.
Bolton said that if Iran continues to pursue uranium enrichment "the next step will be the consideration of sanctions in the security council, and it would be our intention to move forcefully to get those sanctions adopted".
Diplomats said that the first stage would be political and economic sanctions.
The US and its allies believe that Iran is seeking to build a nuclear bomb and George Bush, the US president, said on Friday that Iran "will not be allowed" to get its wish.
After talks in Washington with Tony Blair, the UK prime minister, Bush said: "Our message is give up your nuclear weapon and your nuclear weapon ambitions."
Invitation to dialogue
The draft resolution follows weeks of talks.
Russia and China have led opposition to any mention of sanctions in the resolution.
Vitaly Churkin, Russia's ambassador to the UN, stressed that the new resolution would not threaten sanctions and that it was "an invitation to dialogue" with Iran.
If passed, it would call on Mohammed ElBaradei, the international atomic energy agency director, to give a report on whether Iran has complied by August 31.
Iran has said it will not reply before August 22, nine days before the proposed UN deadline.
Bolton said: "I think the resolution will put the ball back in Iran's court."
The vote seems certain to be passed without difficulty, as all five permanent members support it, removing any threat of a veto.