Iranian President Hassan Rouhani says he wants to reach a deal with world powers on Tehran's nuclear programme in three to six months.
He told the Washington Post he saw a resolution of the issue as a "beginning point" in easing US-Iran relations.
Mr Rouhani said he was fully empowered by Iran's Supreme Leader, Ayatollah Khamenei, to negotiate on the issue.
On Thursday, Iran will hold talks with the P5+1 group of world powers on Tehran's uranium enrichment programme.
In a rare encounter between US and Iranian officials, Foreign Minister Mohammad Javad Zarif will meet US Secretary of State John Kerry as well as diplomats from the UK, France, Russia, China and Germany in New York.
President Rouhani has been in New York this week for the UN General Assembly, and has been giving interviews to US media.
Iranian media has accused CNN of "distorting" comments he made in answer to a question about the Holocaust.
'Everything is possible'
Asked about a timeframe for resolving the nuclear issue,President Rouhani told the Washington Post: "The only way forward is for a timeline to be inserted into the negotiations that is short.
"The shorter it is the more beneficial it is to everyone. If it's three months that would be Iran's choice, if it's six months that's still good. It's a question of months not years."
Despite years of hostility between the US and Iran, Mr Rouhani said that if he and President Barack Obama got together they would both be "looking at the future".
"The notes and letters and exchanges between us are in that direction, and they will continue," he said.
"We need a beginning point. I think that is the nuclear issue."
He added: "After resolution of the nuclear issue there are no impossibilities in term of advancing other things forward. Everything is possible after the settlement."
On Tuesday, Mr Rouhani told the UN General Assembly that he was prepared to engage in "time-bound and results-oriented" talks on the nuclear issue.
Iran has been negotiating with the five permanent members of the UN Security Council, plus Germany, since 2006 about its nuclear programme.
The West suspects Tehran is trying to develop a nuclear weapon, a claim strongly denied by Iran.
President Obama has welcomed the new Iranian president's more "moderate course".
He said the US wanted to resolve the nuclear issue peacefully, but was determined to prevent Iran from developing a nuclear weapon.
On Wednesday, Mr Zarif met French Foreign Minister Laurent Fabius on the sidelines of the General Assembly.
He said they "had a good discussion about the start of nuclear talks and the talks that will take place tomorrow".
Iran's economy has been badly affected by years of sanctions imposed by the UN and Western countries over the nuclear issue.
Tensions were not helped by anti-Israel and anti-Western comments made by the previous president, Mahmoud Ahmadinejad, during his time in office - including frequent denials of the Holocaust.
CNN's Christiane Amanpour asked Mr Rouhani about his position on the Holocaust.
According to a CNN transcript of the interview, he said: "I have said before that I am not a historian personally and that when it comes to speaking of the dimensions of the Holocaust as such, it is the historians that should reflect on it.
"But in general, I can tell you that any crime or - that happens in history against humanity, including the crime that the Nazis committed towards the Jews, as well as non-Jewish people, is reprehensible and condemnable, as far as we are concerned. And just as even such crimes are - if they are to happen today against any creed or belief system or human being as such, we shall again condemn it."
But Iran's Fars news agency said the president never used the word "Holocaust", and gave its own translation of his comments:
"I have said before that I am not a historian and historians should specify state and explain the aspects of historical events.
"However, in general, we fully condemn any kind of crime committed against humanity throughout history, including the crime committed by the Nazis both against the Jews and non-Jews, the same way that if today any crime is committed against any nation, any religion, any people or any belief, we condemn that crime and genocide."