Mr Rouhani also defended the 2015 nuclear deal made between Western states and his country, warning that if the United States abandoned the agreement they would lose the global community's trust.
Ahead of the meeting, Trump told reporters that he had reached a "decision" over the deal without further elaborating.
If the US were to pull out of the deal, Trump would cease to sign future sanctions waivers or de-certify the accord ahead of an October 14 deadline.
Speaking on Wednesday morning in NY, the Iranian President said his regime strives "to build peace and promote the human rights of people and nations".
"An option may be to start enrichment", he said, "not building an atom bomb".
Characterizing it as an agreement negotiated with six world powers, not just the United States, and endorsed by the U.N. Security Council, he said that "it belongs to the worldwide community in its entirety and not only to one or two countries". If Trump does not recertify it, as he has repeatedly suggested he will not, Congress will have 60 days to decide whether to reimpose US sanctions that were lifted when the deal took effect.
Meanwhile, French President Emmanuel Macron has said that he has still not given up on trying to change Trump's view of the deal.
US Secretary of State Rex Tillerson, for his part, said he had a "matter of fact" exchange with his Iranian counterpart, but he said that Washington still has "significant issues" with the nuclear deal.
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"I do believe that if the United States of America breaks the commitment under the JCPOA no other government in the future will be ready and willing to talk or negotiate with the United States of America", he added. That's because "a government that chooses to trample upon her legal and legitimate worldwide commitments - a conversation or negotiation with such a government would be a waste of time".
Rouhani's remarks were a response to Trump's fiery speech Tuesday in which he said that Iran is a "murderous regime" that he put in the same category of rogue nations such as North Korea.
Trump's meeting with Netanyahu was the first of the many world leader confabs he is scheduled to have on the sidelines of the United Nations General Assembly this week.
"And to a large extent, because of what I witnessed, we may do something like that on July 4th in Washington, down Pennsylvania Avenue", Mr. Trump said. But any renewal will only affect change with European support, which the United States is unlikely to receive if it unilaterally withdraws from a successful arms control agreement without cause.
Iranian officials have said the United States will pay a "high cost" for walking away. It was later ratified by the UN Security Council.
Asked whether the agreement could survive without the US, he said "it's a bit early or premature to hold discussions about such questions", adding that the "Europeans want to preserve it".
"If it can not be preserved what will happen then is a very important question that we are analyzing as well as (is) the European Union", Rouhani said, and "other partners" are also analyzing and discussing scenarios.
"One important aspect will be the type of reaction of the European Union should this come to pass", he said.
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