The provocative proposal comes as Iran deals with a new wave of international sanctions -- driven by Washington -- aimed at putting pressure on the Islamic Republic over its nuclear program.
"Toward the end of summer we will hopefully be there for the (U.N.) General Assembly and I will be ready for one-on-one talks with Mr. Obama, in front of the media of course," Ahmadinejad told a conference of Iranian expatriates in Tehran.
"We will offer our solutions for world issues to see whose solutions are better."
Ahmadinejad suggested such a debate last September, which was not taken up by Washington. He said Obama's predecessor, George W. Bush, had declined similar invitations because he was "scared".
Iran, the world's fifth-largest oil producer, says its nuclear program is a peaceful bid to produce electricity.
But its uranium enrichment activities, a process which can have both civilian and military uses, has fed fears in some countries that it is trying to build a nuclear weapon.
In his speech, the president mocked the sanctions and the potential for a military strike against Iran's nuclear facilities, an option that the United States and Israel say they do not rule out.
"Who do you think is going to attack us? The Israeli regime? ... We don't consider the regime in our equations, let alone attacking us," he said.
"They say we'll issue sanctions? Okay, do it. How many resolutions have you issued so far? Four? Make it 4,000," he said to loud applause from the conference.
Both Iran and the United States have indicated willingness to return to nuclear talks which stalled last October, leading to the new sanctions.
Amid the anti-American rhetoric in which he said U.S. policy was based on colonialism and the "law of the jungle", Ahmadinejad said he was ready for talks "based on justice and respect".
"We are ready to hold talks at the highest level," he said. "We have always favored talks, Iranians have never, ever favored war." (Source)