Senior administration officials told reporters on background the White House offered to have "an encounter" between the two, but the Iranians said a possible meeting was "too complicated for Iranians to do at this point."
"There will be no meeting," one official said. "It was clear that it was too complicated for them."
Another senior official said: "The Iranians have an internal dynamic that they have to manage and the relationship with the United States is clearly quite different than the relationship that Iran has with other Western nations."
Rouhani skipped a U.N. luncheon earlier Tuesday, apparently passing up an opportunity to meet with Obama.
Obama, in a speech Tuesday morning to the U.N. General Assembly, used unusually tough language on Syria and welcomed Iran's diplomatic initiative.
Most of the president's speech dealt with the Middle East.
Obama said the Bashar Assad regime used sarin gas on its own people Aug. 21, launching missiles from government-held areas into rebel-held neighborhoods. To suggest Assad did not launch the attack, Obama said, was an "insult to intelligence."
In the face of such an atrocity, "the Security Council had indicated no inclination to act at all," he said.
Assad has agreed to a Russian-U.S. plan to get rid of his chemical weapons, Obama told the delegates.
"Now there must be a strong Security Council resolution that Assad is keeping those agreements," Obama said, with the threat of punishment if he does not.
If the council does not take those actions, "it will show that the United Nations is incapable of enforcing the most basic of international law," Obama said.
Obama stressed peace had to come from the Syrian people, and said the United States was not seeking regime change. But he said Assad could not restore "the status quo" after the civil war ends and continue to lead his people.
On Iran, Obama said he has directed U.S. Secretary of State John Kerry to follow up overtures from the Iranians to develop a new relationship.
The president said there has been much distrust between the United States and Iran since the 1979 Islamic Revolution.
"I don't believe this difficult history can be overcome overnight," Obama said, but the two countries have to make a start.
Obama said the United States is determined not to allow Iran to develop a nuclear weapons, and friendly words would have to be followed by verifiable actions.
Rouhani has engaged in several weeks of charm diplomacy suggesting a desire to improve relations with the United States and the West in general.
The United States broke diplomatic relations with Iran April 7, 1980. Switzerland represents U.S. interests in Tehran while Pakistan represents Iranian interests in Washington.
The White House repeated Monday Obama was "open to engagement" with Rouhani.
"He's exchanged letters with Rouhani," deputy national security adviser Ben Rhodes told reporters traveling with the president to New York.
Washington and U.S. allies allege Iran is well along toward developing a nuclear weapon, but Tehran insists its nuclear activities are only to produce electricity and for medical research.
Western diplomats predict Rouhani's speech later Tuesday will be conciliatory and include an important gesture, such as an acknowledgment of the Holocaust -- a sharp contrast to the angry, Holocaust-denying diatribes of his predecessor, Mahmoud Ahmadinejad.
Rouhani is to be accompanied at the General Assembly by Ciamak Morsadegh, Iran's only Jewish member of Parliament.
Kerry is to meet his Iranian counterpart, Mohammad Javad Zarif, Thursday in the first face-to-face foreign minister exchange between the two countries since 2007 and the first official meeting on that level since 2000.
Zarif, who got his doctorate in international law and policy from the University of Denver, is to join nuclear talks in New York with the United States and five other world powers -- Russia, China, Britain, France and Germany.
It was not immediately clear if Kerry and Zarif would break off from the group and meet one-on-one.