"We asked that the consultations be postponed not in order to revise the text but in order that we continue informal consultations that will take place in different configurations," Britain's UN envoy Emyr Jones Parry said.
He said that he and his French colleague, Jean-Marc de La Sabliere, felt there was no point in amending their draft if an agreement was not in sight.
"If there's no prospect for an agreed conclusion, we won't be amending the text," Mr Jones Parry said.
Mr Jones Parry called the latest discussions "not as positive as we would have wished."
Earlier a Western diplomat who requested anonymity said the formal council meeting was postponed to take into account Russian objections to the Franco-British draft and that no new date has been set for a formal meeting.
"The Russians want a more general text and no reference to the Iranian program being a threat to international peace and security, which could imply that the council might have to resort to sanctions," he said.
Iran defiant
The US and other countries have accused Iran of aiming to develop nuclear weapons.
The Security Council is debating a response to Tehran's defiance to demands that it halt uranium enrichment activities and open its doors to inspectors from the International Atomic Energy Agency.
Western powers see adoption of the Franco-British non-binding statement in the Security Council as the first step in a graduated response that could ultimately lead to sanctions against Tehran.
But Russia and China, which have close economic and energy ties with Tehran, oppose sanctions and insist on the IAEA retaining the lead role in the issue.
Iran denies the claims that it is seeking nuclear arms and insists that as a signatory of the nuclear Non-Proliferation Treaty it has a right to conduct uranium enrichment.
The 15-member Security Council had been due to review the Franco-British draft as well as a broader strategy to deal with Tehran.
Bush warning
Meanwhile US President George W. Bush has again warned against a nuclear-armed Iran that "could blackmail the world."
But Bush also reaffirmed that he wanted a diplomatic solution and that his government would continue to let Britain, France and Germany lead international talks with Iran.
Iran says it will not be bullied by the United States over its nuclear program and is not worried about being referred to the UN Security Council.
"We emphasise that nuclear technology and the nuclear fuel cycle is our absolute right. The nation, I and other officials will not yield to America's bullying language by any means," Iran’s supreme leader
Ayatollah Ali Khamenei said in a televised speech.
Iran has said it wants to master technology over the whole nuclear cycle from uranium ore to fuel.
"They are threatening us with the Security Council as if the
Security Council is the end of the world," Ayatollah Khamenei said.
"We had experience of the Security Council (threats) at the time of the (Iranian) war with Iraq. Whatever is against the interest of the country we will not accept," he said, referring to Iran's eight-year war with its western neighbour.