"We still have some possibility of coming to an agreement ... but that may require a lot of flexibility on both sides," he said.
"We will not simply bow down to the evolving consensus if we do not agree."
Clinton responded by saying the US-led drive to impose more sanctions on the Islamic Republic was the only way to bring it back to the negotiating table.
"Only after we pass sanctions in the security council will Iran negotiate in good faith," Clinton said.
She urged countries to be cautious about Iran's assurances that it had only peaceful intentions.
"We have seen an Iran that runs to Brazil, an Iran that runs to Turkey and an Iran that runs to China, telling people different things to different people to avoid international sanctions," Clinton said.
She echoed Amorim when she said both shared the goal of preventing Iran from becoming a nuclear weapons country, but said the two differed in how to attain it.
She said the US believed sanctions are "the best way to avoid conflict and arms races that could disrupt stability and the peace and the oil markets of the world."
Lula, who has upset Washington by pursuing close ties with Tehran, has repeatedly voiced caution over the drive by the US, Britain, France and Germany for new sanctions.
However, a senior US official, speaking to reporters on Clinton's plane, said the Brazilians told Clinton their position was not "etched in stone" and said the two countries would continue talking.
The official said that if Lula's planned May visit to Tehran occurs after a security council sanctions vote, it could "take on a different cast", suggesting Lula could act as an intermediary to urge Iran back to talks.
Lula said Brazil would "not support any move by Iran to go beyond the peaceful use of nuclear energy".
He said that he planned to have a "frank discussion" on the subject with Iranian President Mahmoud Ahmadinejad when he visits Tehran.
While most attention has been focused on getting support from Russia and China for sanctions, because they hold veto power over any UN resolution, the US had hoped to win over key non permanent security council members such as Brazil and Turkey to present a united front on the Iran nuclear stand-off.
Diplomats in New York told Reuters news agency this week that the western powers had prepared a revised draft proposal for a fourth round of sanctions against Iran.
Speaking on condition of anonymity because the discussions are still taking place, the diplomats said Russia had expressed a willingness to negotiate on the elements for a new UN sanctions resolution but China, which relies on Iran for much of its energy, had not responded.
The sanctions are said to target the country's powerful Revolutionary Guard and toughen existing measures against its shipping, banking and insurance sectors.
Tehran has denied the accusation that it is building a nuclear bomb, saying its programme is purely for peaceful purposes.