Obama, who broke with former US policy of isolating Tehran, said it would be hard to "overcome decades of mistrust" but he had made clear to Iran's leaders and people that the United States was prepared to move forward in relations with Iran.
"But it is clear to all concerned that when it comes to nuclear weapons we have reached a decisive point.
"This is not simply about America's interests. It is about preventing a nuclear arms race in the Middle East that could lead this region and the world down a hugely dangerous path."
In an apparent reference to Israel, believed to be only nuclear-armed power in the Middle East, Obama said he understood protests "that some countries have weapons that others do not."
He added that this was why he reaffirmed America's commitment to seek a nuclear-weapons-free world.
He said that "any nation — including Iran — should have the right to access peaceful nuclear power if it complies with its responsibilities under the nuclear Non-Proliferation Treaty."
Iran has resolutely maintained its right to a nuclear programme which it insists is purely for peaceful means.
This has put it on a collision course with Western powers who suspect it of seeking nuclear weapons.
Iran's arch-foe Israel has refused to rule out a military strike to ensure Tehran does not become a nuclear-armed nation.
