Tehran described the claims, made by Israeli prime minister Benjamin Netanyahu on Monday, as a show of "threadbare charlatanism".
It came after the United States supported Israel's claims, describing them as "compelling" - though they have received a much cooler welcome within Europe.
Mr Netanyahu says the documents show that its bitter enemy Iran attempted to develop a nuclear bomb in the decade before the 2015 deal, especially before 2003.
Although he gave no explicit evidence that Iran has violated the landmark agreement, he said it showed Iran had clearly lied in the past and could not be trusted.
Iran has denied ever pursuing nuclear arms.
Mr Netanyahu said he would share the newly uncovered information about Iran's 'Project Amad' - amounting to 55,000 pages of documents and 183 CDs - with Western allies and the international nuclear agency.
"We can now prove that Project Amad was a comprehensive programme to design, build and test nuclear weapons," he said.
"We can also prove that Iran is secretly storing Project Amad material to use at a time of its choice to develop nuclear weapons."
Ahead of Mr Netanyahu’s presentation, Iran’s foreign minister, Mohammad Javad Zarif, mocked the Israeli leader by tweeting a photo of his 2012 UN speech in which he used a cartoon-like drawing of a bomb to argue against Iran’s nuclear programme.
The state-run IRNA news agency on Tuesday quoted the spokesman, Bahram Ghasemi, as saying Netanyahu's speech was part of "fruitless efforts of a bankrupt and scandalous liar."
Mr Netanyahu had fought for the denuclearisation deal with Iran while former US President Barack Obama was negotiating it, but he has been a leading critic since it was signed.
He says it does not provide sufficient safeguards to prevent Iran from reaching a nuclear weapons capability.
The Israeli leader has found a welcome partner in Mr Trump, who has called the agreement "the worst deal ever".
The US president has signalled he will pull out of the agreement by May 12 unless it is revised, but he faces intense pressure from European allies not to do so.
US Secretary of State Mike Pompeo said the documents obtained by Israel from inside Iran "show beyond any doubt that the Iranian regime was not telling the truth".
In a statement, US Press Secretary Sarah Huckabee Sanders said the "information provides new and compelling details about Iran's efforts to develop missile-deliverable nuclear weapons".
"These facts are consistent with what the United States has long known: Iran has a robust, clandestine nuclear weapons program that it has tried and failed to hide from the world and from its own people", she said.
However, the UK stood by its signing of the 2015 deal.
A Downing Street spokesperson said: "We have never been naive about Iran and its nuclear intentions.
"That is why the IAEA inspection regime agreed as part of the Iran nuclear deal is one of the most extensive and robust in the history of international nuclear accords
"It remains a vitally important way of independently verifying that Iran is adhering to the deal and that Iran’s nuclear programme is exclusively peaceful."
The European Union’s foreign affairs chief said Netanyahu’s latest allegations do not appear to show Tehran is currently violating the 2015 international nuclear agreement.
Federica Mogherini said: "What I have seen from the first reports is that Prime Minister Netanyahu has not put into question Iran’s compliance."
She insisted it is "first and foremost" the International Atomic Energy Agency that must make the assessment whether Iran is abiding by the deal, because "the IAEA is the only impartial, international organisation that is in charge of monitoring Iran’s nuclear commitments".
Yoel Guzansky, senior fellow at the Institute for National Security Studies, an Israeli think tank, said Mr Netanyahu's message was unlikely to change minds in Washington or Europe.
Although Iran has threatened to withdraw from the deal if the US pulls out, Guzansky said Tehran would likely be more cautious, and much will depend on the reactions of major companies.
"It's in Iran's interest to stay in the agreement," he said. "It matters if Renault, Total and other European companies will continue to do business with Iran."