In his first news conference since Friday’s vote, Hassan Rouhani also described as unfair sanctions imposed on the country over the issue.
The president said Tehran would not suspend its uranium enrichment activities.
The West suspects Iran of trying to build nuclear weapons. Tehran says its programme is solely for peaceful purposes.
At the news conference, which covered a wide range of issues, Hassan Rouhani also said his government would work towards “constructive interaction with the world”.
He thanked Iranians for “choosing moderation”, saying he would not forget his election promises.
Hassan Rouhani, a long-standing political figure in Iran, won just more than 50% of the vote in the election, avoiding a run-off vote.
Iran’s president has limited powers, with key policy decisions being taken by the Supreme Leader, Ayatollah Ali Khamenei.
“Our nuclear programmes are completely transparent,” Hassan Rouhani told a packed hall in the capital Tehran.
“But we are ready to show greater transparency and make clear for the whole world that the steps of the Islamic Republic of Iran are completely within international frameworks,” he said.
But he stressed that he would oppose halting Iran’s uranium enrichment – a key stumbling block in the continuing talks between Tehran and world powers.
Last month, the UN nuclear watchdog said Iran had installed hundreds of new centrifuges at its Natanz plant.
The International Atomic Energy Agency (IAEA) again expressed concern about the “possible military dimensions” of Iran’s nuclear programme.
But it said there had not been much growth of the most sensitive nuclear material – uranium enriched to 20%.
Iran has been the target of four rounds of UN sanctions and numerous UN Security Council resolutions calling on it to cease enrichment work.
Israel has threatened to carry out air strikes on its long-time foe if its enrichment activities do not stop.
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