The interview with the president aired ahead of his trip to the Mideast Tuesday night -- a visit aimed at repairing the rocky relationship between the U.S. and the world's 1.5 billion Muslims.
Obama's trip to the region is also aimed at deterring Islamic extremists.
The president told the BBC that he plans to use diplomacy to persuade Tehran not to build nuclear weapons.
"What I do believe is that Iran has legitimate energy concerns, legitimate aspirations," Obama said.
Iranian state television reported Obama's comments as "recognizing the rights of the Iranian nation," which is how the country refers to its nuclear program, the AP reported.
Obama said the global community "has a very real interest" in halting a nuclear arms race. Iran claims it will use nuclear energy for electricity but the U.S. and other governments suspect Iran is using the power to build weapons.
"Although I don't want to put artificial timetables on that process, we do want to make sure that, by the end of this year, we've actually seen a serious process move forward," Obama said. "And I think that we can measure whether or not the Iranians are serious."
The President said Tehran had until year's end to prove it wants to negotiate with the U.S. about its nuclear program and indicated that he is willing to seek bolstered international sanctions against the country if it is uncooperative.
The interview is a preview of Obama's speech in the Cairo on Thursday, the highlight of his trip to Egypt and Saudi Arabia. Obama plans to speak about relations between Americans and Muslims abroad.
"What we want to do is open a dialogue," Obama said. "You know, there are misapprehensions about the West on the part of the Muslim world. And, obviously, there are some big misapprehensions about the Muslim world when it comes to those of us in the West."