A top US diplomat has said he expects European states to prepare a binding UN resolution on Iran's nuclear programme that could allow for sanctions.
Mr Burns said the world must "send a stiff message" to Iran
However, US Under Secretary of State Nicholas Burns added that diplomacy still offers the best solution to the crisis over Iran's nuclear ambitions.
Senior diplomats from the Council's five permanent members ended a meeting in Paris on Tuesday without agreement.
A meeting of foreign ministers is due next week to seek a unified stance.
The talks in Paris between representatives from the US, UK, Russia, China, France were held to discuss Friday's report by the UN's nuclear watchdog that Tehran had ignored calls to halt uranium enrichment.
Iran says it needs the enriched uranium as fuel for nuclear power plants - and denies US accusations that it is trying to build a nuclear bomb.
The different parties at the Paris talks expressed "their concern about the development" of Iran's nuclear programme, French Foreign Ministry spokesman Jean-Baptiste Mattei told the Associated Press news agency.
However, there was no consensus on what action to take.
The US, UK and France want the Security Council to adopt a so-called "Chapter 7" resolution, ordering Iran to suspend enrichment - and threatening it with sanctions if it disobeys.
Chapter 7 Security Council resolutions are binding on all UN members, but do not automatically lead to sanctions or military action. Further decisions would be needed for such measures.
Before a Chapter 7 resolution is passed, the Council has to agree that there is a threat to "international peace and security".
China and Russia are yet to support such a resolution and are opposed to sanctions against Iran.
Mr Burns expressed frustration at their stance, saying: "It's time for countries to take responsibilities, especially those countries that have close relationships with Iran."
He added that there would be international support for sanctions against Iran "within a month or two or three".
Diplomacy towards Iran, he said, needed to be "hard-edged".
With the need for international unity seen as paramount, the stage seems set for more long and difficult diplomatic negotiations, correspondents say.
Iranian Foreign Minister Manuchehr Mottaki said earlier Russia and China had told Iran they were "against sanctions and military attacks".
Iran says its nuclear programme will only serve its energy needs
"There is a very wrong assumption held by some that the West can do anything it wants through the Security Council," he told Tehran newspaper Kayhan.
Iran has said already that it will dismiss any UN resolution regarding its nuclear programme.
There is growing anxiety about the apparently fading prospects of making Tehran stop uranium enrichment - and of the risk of US military action if it fails to do so.
An IAEA report on Friday said that Iran had failed to comply with a 30-day Security Council deadline to stop uranium enrichment.
On Tuesday, Iran's atomic energy chief said Tehran had enriched uranium to 4.8% - which experts say is a low level used in atomic power reactors.
Iran on Monday strongly criticised the US at the UN, accusing Washington of threatening to launch a military strike against its nuclear facilities.
US President George W Bush has refused to rule out military action against Iran, but has repeatedly insisted that the dispute be resolved diplomatically.