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Rouhani said the four-point program stipulated that Iran should not seek nuclear weapons, should abide by regional peace, help to contribute to peace, and, in exchange, the US would lift all sanctions against Tehran and allow Iranian exports "immediately."
Tehran balked when Trump doubled down on increasing sanctions in two announcements he made over 24 hours, the Iranian president said.
"Then I told the Europeans, now (with) what he has said, how can we accept it?" Rouhani added in his televised speech.
Macron and UK Prime Minister Boris Johnson were seen urging Rouhani to meet Trump, in a rare three-way meeting.
In a video that captured the encounter on the sidelines of the General Assembly, UK Prime Minister Boris Johnson is heard telling Rouhani: "You need to be on the side of the swimming pool and jump at the same time."
In an interview with CNN's Christiane Amanpour in September, Iranian Foreign Minister Javad Zarif said Iran would be open to negotiating a new deal, that may see Iran's "permanent denuclearization" in exchange for Congress-ratified sanctions relief.
Tehran had previously said repeatedly that it would not be willing to renegotiate the 2015 nuclear deal which Trump withdrew from in May 2018.
In a joint press conference with Italian Foreign Minister Luigi Di Maio on Wednesday, US Secretary of State Mike Pompeo called on the European Union to "stand united against Iranian aggression." But he added that the Trump administration remained "hopeful" about talks with Iran.
"European nations have begun to wake up to the fact that Iran is the aggressor and not the aggrieved," said Pompeo.
"We remain hopeful that there will be an opportunity to discuss with the Iranians the path forward," he later added.
CNN's Schams Elwazer and Sarah Dean in London contributed to this report.