But he balanced the offer with a sharp rebuke to Washington and its allies over Iran's nuclear program. He reiterated that Iran would never abandon its advances in uranium enrichment in exchange for offers of easing sanctions or other economic incentives.
The nuclear issue "is closed," he told a news conference.
Obama has urged a "serious process of engagement" after Iran's elections in an effort to end a nearly 30-year diplomatic chill. However last week, the American leader said the U.S. was prepared to seek deeper international sanctions against Tehran if it did not respond positively to the attempts to open negotiations on its nuclear program. Obama set a year-end deadline for Iran to show it wanted to engage with Washington.
The tough talk on nuclear negotiations following Iran's test last week of a long-range missile appear aimed at burnishing Ahmadinejad's hard-line credentials in the election campaign against another conservative and two pro-reform candidates.
His offer of to debate Obama could also be campaign posturing before the June 12 vote. But it does put Ahmadinejad on record as supporting a potentially groundbreaking encounter following Obama's offer for dialogue.
Ahmadinejad said that, if re-elected, he would be open to "debate global issues as well as world peace and security" during the U.N. General Assembly in September.
There was no immediate reaction from Washington.
On the nuclear issue, Ahmadinejad ruled out talks with the U.S. He said Iran's stand is "crystal clear" and Tehran would only discuss the subject within the framework of the U.N. nuclear watchdog, the International Atomic Energy Agency.
Ahmadinejad has often denounced the West for trying to pressure Iran to give up it uranium enrichment program, a process that can produce fuel for both nuclear energy and nuclear weapons. Tehran insists it is only to fuel peaceful reactors, but the West worries could lead to nuclear weapons development.
His latest comments appear to be part of a campaign strategy to portray himself as the only candidate capable to defending Iran's nuclear technology.
Last week, he accused his reformist predecessor, Mohammad Khatami, of bringing "humiliation" on Iran by agreeing to suspend uranium enrichment from 2003-5 as a confidence-building measure with the West.
That also served as a direct shot at Ahmadinejad's main reformist challenger, Mir Hossein Mousavi, who is backed by Khatami.
Ahmadinejad also faces another hard-liner, former Revolutionary Guard commander Mohsen Rezaei, and a moderate, former parliament speaker Mahdi Karroubi, in the four-way race.
Mousavi attacked Ahmadinejad's handling of the economy at a campaign rally in the northwestern city of Tabriz on Monday. Unemployment is rising and inflation has reached 25 percent, making the economy one of the president's most vulnerable points among voters.
"Iran is a rich country. Poverty is not our destiny. It's the government's mismanagement that has taken us here," Mousavi told tens of thousands of cheering supporters.
The campaign took a bitter turn over the weekend when reformists accused Ahmadinejad's supporters in the Islamic regime of blocking the popular social networking site Facebook, which has become an important tool to mobilize Iran's crucial youth vote.
More than half Iran's population was born after the 1979 Islamic Revolution and young voters represent a huge potential bloc for pro-reform candidates.
Ahmadinejad sidestepped questions about whether authorities ordered a Facebook block late last week. But he said he believed "in maximum freedom of expression."
"There are many Web sites active in the world that can be accessed in Iran. Many Web sites are against the government," he said, adding that officials "don't need to shut any sites shut down."
But Iran has cut off access to many blogs and Web sites critical of the Islamic regime and its ruling clerics. Media groups and others have strongly criticized Iran's clampdown on the web.
Mohammad Ali Abtahi, a former vice president and a top adviser to Karroubi's campaign, called the Facebook block "painful news for young and educated Iranians."
"(Ruling authorities) would only like their voice heard," he wrote in an e-mailed protest, claiming his own Facebook site had attracted more than 3,000 followers. "Any other voice (for them) is intolerable."