Ahmadinejad made the claim about Iran's nuclear prowess in a speech at a rally marking the 31st anniversary of the Islamic revolution.
"By God's grace ... it was reported that the first consignment of 20 per cent enriched uranium was produced and was put at the disposal of the scientists," Ahmadinejad said.
His claim comes just two days after Iranian officials said they had started the higher enrichment process at the Natanz nuclear facility, and the president added: "In the near future we will treble its production."
John Large, an independent nuclear engineer, shared Gibbs's views.
He told Al Jazeera from London that it was simply not possible for Tehran to have completed the 20 per cent enrichment of any of its uranium stockpile in such a limited time.
"Even to produce tiny amounts, representative amounts, of uranium enriched to 20 per cent would be an impossible task," he said.
"For Iran to actually move to a 20 per cent enrichment would mean it would have to devote its somewhat limited enrichment facilities and the gas facilities it requires to prepare for that.
"You can't have a complex material manufacturing process like this and suddenly change the policy at whim."
But Mohammad Marandi, a professor of political science at Tehran University, said he was "pretty confident" that Ahmadinejad's announcement was truthful.
"Every time in the past that Iran has made an announcement in Western circles many experts in the West have been sceptical," he said
"But at the end of the day it has turned out to be true, with regards to Iran's satellite, with regards to the enrichment of uranium to 3.5 per cent."
'Anything but peaceful'
Despite Washington's scepticism over Ahmadinejad's claim, Gibbs and other US officials said Iran's behaviour on the nuclear front was disturbing and in violation of numerous UN sanctions.
The government, which on Wednesday imposed new sanctions on affiliates of Iran's Revolutionary Guards Corps, is pressing hard to get fresh penalties imposed on Iran at the UN Security Council.
PJ Crowley, a spokesman for the US state department, said that even if untrue, Ahmadinejad's claim "further solidifies our impression and that of the international community that Iran's nuclear intentions are anything but peaceful".
But Ahmadinejad, in his speech on Thursday, repeated that Iran's nuclear programme was not aimed at producing a nuclear weapon.
"If we wanted to manufacture a bomb, we would announce it ... our nation has the courage to explicitly say it and build it and not fear you," he said.