Ahmadinejad made the announcement in a speech to hundreds of thousands of cheering Iranians at a rally to mark the anniversary of the 1979 Islamic Revolution.
Just two days earlier, Iran said it had begun enriching uranium to higher levels than before, raising fears it may be moving closer to the ability to produce material for a nuclear weapon.
But the president insisted Iran had no intention of building nuclear weapons and said if it intended to, it would say so openly.
Iran previously said it had begun enriching uranium to 20 percent purity to power a research reactor for production of medical isotopes, up from 3.5 percent previously. But the international community has demanded a halt to all enrichment activity because the same process is used to produce weapons-grade material if it is enriched to a level of 90 percent.
Experts say that from 20 percent enrichment, Iran could make a quick leap to weapons-grade uranium.
Ahmadinejad did not say how much of the more highly enriched uranium had been produced. But David Albright of the Washington-based Institute for Science and International Security said that any 20-percent enriched uranium produced just a few days after the start of the process would be "a tiny amount."
"I want to announce with a loud voice here that the first package of 20 percent fuel was produced and provided to the scientists," Ahmadinejad said. He reiterated that Iran was a "nuclear state".
The claim of new progress in Iran's nuclear programme came a day after the US Treasury Department imposed new sanctions. It froze the assets in US jurisdictions of a Revolutionary Guard general and four subsidiaries of a construction firm he runs for their alleged involvement in producing and spreading weapons of mass destruction.
The US said the elite Revolutionary Guard military force has consolidated control over broad swaths of the Iranian economy, displacing ordinary Iranian businessmen in favor of a select group of insiders. It has also been the prime force leading a crackdown on internal opposition to the country's disputed June 12 presidential election.
The international community also appears to be moving closer to imposing new U.N. sanctions on Iran over the nuclear program.
British Prime Minister Gordon Brown, speaking at a meeting of European Union leaders in Brussels, warned Iran that while the West and others still favor a dialogue with Tehran, "the patience of our countries is not inexhaustible."
"Iran can either pursue a civilian nuclear program, respect human rights and earn the trust and respect of the international community, or it can move ahead with its nuclear weapons program, trample on human rights and be isolated and ostracized on the wrong side of history, outside the international community," Brown said.
The United States and some of its allies suspect Tehran is using its civilian nuclear program as a cover to build nuclear weapons but Tehran denies the charge, saying it has only has peaceful intentions.
Addressing the crowd, Ahmadinejad swore "the Iranian nation will never give in to bullying and illogical remarks" from the West.
"We have the capability to enrich uranium more than 20 percent or 80 percent but we don't enrich (to this level) because we don't need it," he added. "When we say we do not manufacture the bomb, we mean it, and we do not believe in manufacturing a bomb."
"If we wanted to manufacture a bomb, we would announce it," he said.
Tehran says it wants to enrich uranium to 20 percent as a part of a plan to fuel its research reactor which provides medical isotopes to hundreds of thousands of Iranians undergoing cancer treatment.
But the West says Iran is not capable of turning the uranium into the fuel rods needed by the reactor. Instead it fears that Iran wants to enrich the uranium to make nuclear weapons.
A confidential document from the UN nuclear agency shared Wednesday with The Associated Press said Iran's initial effort at higher enrichment is modest, using only a small amount of uranium and a fraction of its capacities.
Western powers say Iran has rejected an internationally endorsed plan to defuse the situation by having Iran export its low enriched uranium for further enrichment abroad and returned as fuel rods for the Tehran reactor.
Iran, in turn, asserts it had no choice but to start enriching to higher levels because its suggested changes to the international plan were rejected.
The president said Iran will triple the production of its low-enriched uranium in the future.
"God willing, daily production (of low enriched uranium) will be tripled," he said.
