The official said that an offer in this regard was made by the US, which Iranian officials turned down saying it was "too complicated" for them at this point of time.
"We did not have any plan for a formal bilateral meeting here. We indicated that the two leaders could have had a discussion on the margins if the opportunity presented itself.
"The Iranians got back to us; it was clear that it was too complicated for them to do that at this time given their own dynamic back home," the official, who spoke on condition of anonymity, told mediapersons.
However, the US would continue with its direct talks with Iran through the Secretary of State John Kerry as announced by Obama in his address to the UNGA on Tuesday.
"I am directing John Kerry to pursue this effort with the Iranian government in close cooperation with the European Union, the United Kingdom, France, Germany, Russia and China," Obama said.
The official cited "complicated dynamics in Iran" surrounding the relationship with the US as reason for the Iranians to turn down the offer and clarified that there was no proposal for a bilateral between the two president.
"I think part of what has strengthened the United States in the international community in terms of our unity is the president's openness to engage Iran, and that's what we've indicated from the beginning of the administration. I think that indicates that we're ready to solve this problem, and that's what we've indicated not just when we came into office, but most recently with President Rouhani," he said.
"We had discussions at a working level with them and ultimately it became clear that that was too complicated for them at this time," the official said.
"This was not a formal offer that then came back because it's too complicated. This was some conversations that were taking place about the possibility of an informal, brief encounter," the senior administration official said.
The US had, in fact, proposed for a chance encounter like handshake on the margins of UNGA.
There had been signs that the US and Iran would have the highest diplomatic contact since before Iran's 1979 Islamic revolution to try to settle Tehran's nuclear issue.