Obama also told the Associated Press that Iranian President Hassan Rouhani had staked his credibility on dialogue and it was up to the United States to see if he had the political weight to follow through.
The president's timetable contrasts with that of Israeli Prime Minister Benjamin Netanyahu who has warned that Iran has been building faster centrifuges to enrich uranium which would allow it to jump across an Israeli red line within "weeks."
Obama, who spoke to Rouhani in a historic telephone call last week, and then hosted Netanyahu at the White House on Monday, also said it remained to be seen if the Iranian president could follow through on his initiative.
"He is not the only decision maker he is not even the ultimate decision maker," Obama told the AP.
The president was referring to the fact that final authority on the nuclear issue in Iran rests with Supreme leader Ayatollah Ali Khamenei.
Earlier, Khamenei offered qualified backing to Rouhani's visit to the UN last week but criticized some aspects of his performance - a possible reference to the phone call with Obama.
"We support the diplomatic initiative of the government and attach importance to its activities in this trip," Khamenei told military commanders and graduating cadets in remarks reported by his website, Khamenei.ir.
However, he added -- without elaborating -- that "some of what happened in the New York trip was not appropriate... although we trust in our officials."
The September 27 telephone conversation, the first diplomatic contact between Iranian and US presidents, broke 34 years of icy relations between Washington and Tehran since its 1979 Islamic revolution.
Netanyahu warned in a speech to the UN this week that Israel would use military action to act alone to defend itself if necessary against Iran's nuclear program.
But it appears highly unlikely Israel could take any action while nuclear talks involving the United States and world powers with Iran are taking place.
Obama has said Washington must "test" Iran's offer of serious talks on its nuclear program.
The next round of talks takes place in Geneva later this month.
Iran denies its nuclear program is meant to produce weapons. Obama says the Islamic Republic must verifiably prove its intentions are "peaceful" in any deal that would ease US sanctions on Tehran.