The two leaders spoke by telephone at the end of Rouhani's visit to the world's largest diplomatic gathering last year, but neither side said a call or meeting had been scheduled this time.
"Is it written as a rule somewhere that two presidents must always communicate telephonically?" a smiling Rouhani quipped to reporters when asked a second question about the lack of contact.
"At one point it just so happened ... It doesn't mean that every trip (when) we come here, our departure must culminate in a phone call," he told the news conference at a New York hotel.
Iran and the United States broke off diplomatic relations in the aftermath of the 1979 Islamic revolution but have held increasingly frequent talks as they work on an agreement to address international concerns over Tehran's nuclear program.
Yet any hopes of a presidential meeting were dashed Thursday when Obama returned to Washington after days in New York drumming up support for his air campaign against jihadists in Iraq and Syria.
Iran, a close ally of Damascus, has criticized the Syria strikes, blaming more than a decade of US bombing raids for fueling, not eradicating extremist groups in the Middle East and South Asia.
But Rouhani delivered a passionate call for Iran and the United States to slowly rebuild trust, saying it was not written in stone that Iranian-US relations must always be driven by conflict.
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"One day this will change," he said. Both sides "must step by step lay a solid foundation on which to build a better future."
Rouhani expressed hope that an agreement to allay Western concerns over Tehran's nuclear program in return for an end to sanctions would be first step towards rebuilding years of distrust.
"Trust is a very long ladder but ultimately the truth is that if we take step by step... we will reach a rooftop from which we can clearly view the positive benefit... for both nations," he said.
In this wider framework of striving for closer relations in the future, Rouhani said telephone calls were "somewhat meaningless."
"Because of the sensitivity that still exists between the two countries, such action would only be fruitful," when done according to a precise plan with clear objectives, he said.
The reform-minded leader denied that human rights were worsening in Iran and said he remained committed to his pledges for civil rights on which he campaigned for election last year.
US newspaper headlines have focused on three US citizens being held in Iran, a former Marine arrested three years ago accused of espionage, a Christian pastor and a Washington Post correspondent.
In June, a British-Iranian woman, Goncheh Ghavami, 25, was also arrested when she went to watch a men's volleyball game.
Rouhani said arrests should not be blown out of proportion, saying that the judiciary must investigate and that any foreigner placed under detention must have competent legal counsel.