"We have always been in favor of talks. Iran is ready today to hold talks based on justice and mutual respect," he added.
Washington said it could not confirm Ahmadinejad's announcement.
"Obviously it has been some time since our last p5+1 talks. We've been quite clear on what we are looking for. But we do support this dialogue, and as we've said often there's two tracks here and the door does remain open," State Department spokesman Mark Toner told a news briefing.
After the last round of talks, which also took place in Istanbul, Ashton called the nuclear discussions with Iran disappointing, saying no further meetings were scheduled.
Iran has been hit by international sanctions for refusing to halt its sensitive nuclear activities. Ahmadinejad said Iran had no intention of stopping its nuclear work.
"Our nuclear activities are legal ... and under the supervision of the International Atomic Energy Agency," he said in Istanbul, where he attended the conference of "least-developed countries."