But he added that "it's time now for Iran to send some signals that it wants to act differently".
And he warned that any thaw in ties is "not going to happen overnight", because "there's been a lot of mistrust built up over the years".
"And it's important that, even as we engage in this direct diplomacy, we are very clear about certain deep concerns that we have as a country.
"That Iran understands that we find the funding of terrorist organisations unacceptable, that we're clear about the fact that a nuclear Iran could set off a nuclear arms race in the region that would be profoundly destabilising," said Obama.
Obama pledged during the 2008 White House race to break with what he described as predecessor George Bush's unproductive and confrontational policy towards Iran, and ordered a review of relations shortly after taking office on January 20.
The west suspects Iran of secretly trying to build a nuclear weapon and fears the technology used to launch a space rocket could be diverted to developing long-range ballistic missiles capable of carrying nuclear warheads.