In an interview filmed on Friday with ABC News, Mr Ahmadinejad said the report in the Times newspaper was "fundamentally not true".
Mr Ahmadinejad said criticism of Iran's nuclear programme had become "a repetitive and tasteless joke".
Iran says its nuclear enrichment programme is for peaceful purposes.
The BBC's Jane O'Brien in Washington says the interview offered a rare opportunity to see an Iranian leader being questioned by the US media.
But Mr Ahmadinejad's answers gave little indication that his administration is moving towards a more conciliatory position, says our correspondent.
'Fabricated papers'
The Times reported last week that it had obtained a document, dating from 2007, describing a four-year plan by Iran to test a nuclear trigger using uranium deuteride.
The product can be used as a neutron initiator: the component of a nuclear bomb that triggers an explosion.
In his first public response to the report, Mr Ahmadinejad said the accusations were "fundamentally not true".
He dismissed the documents, saying: "They are all a fabricated bunch of papers continuously being forged and disseminated by the American government."
When asked if there would "be no nuclear weapon in Iran, ever", Mr Ahmadinejad said his view was already known.
"You should say something only once. We have said once that we don't want a nuclear bomb. We don't accept it."
'Bullying'
Iran is already subject to three sets of UN sanctions for its refusal to suspend its uranium enrichment programme.
It is at risk of further sanctions after it rejected a deal to send low-enriched uranium abroad to be refined into fuel for a research reactor.
Mr Ahmadinejad said Iran would welcome talks "under fair conditions".
"We don't welcome confrontation, but we don't surrender to bullying either," he said.
"If you are saying you are going to impose sanctions, then go and do it."
Mr Ahmadinejad also rejected criticism of Iran's human rights situation and allegations of mass arrests following the elections which returned him to office in June.
"These things have to do with the judiciary. We have good laws. There is the judge. These people have got lawyers. These are not political questions."
He said people in Iran had more freedom than in the US.
The ABC interview took place before the latest protests held at the funeral of the influential dissident cleric, Grand Ayatollah Montazeri.
Iran says its uranium enrichment programme is for purely peaceful purposes, aimed at generating electricity so that it can export more gas and oil.
But the US and its allies say it could be used to develop weapons.
