Hassan Rouhani won more than 50% of the vote in Friday's election. Photo: BBC

In his first news conference since Friday's vote, Mr Rouhani, 64, also described as unfair sanctions imposed on the country over the issue.

And he 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, Mr Rouhani also said that:

• His government would work towards "constructive interaction with the world", thanking Iranians for "choosing moderation"
• Efforts to end continuing fighting in Syria and restore stability must rest with "the Syrian people"
• The economy would be his main priority
• Relations between Iran and the US were "an old wound that needs to be healed"

The conference ended abruptly when a man in the audience shouted that reformist leader Mir Hossein Mousavi, who is currently under house arrest, should be president.

Mr Rouhani, a long-standing political figure in Iran, won just more than 50% of the vote in the election, avoiding a run-off vote.

Key stumbling block

"Our nuclear programmes are completely transparent," Mr 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) - which has been pushing Tehran to be transparent about its nuclear activities - expressed concern about the "possible military dimensions" of the 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.

But on Monday, Mr Rouhani said: "The sanctions are unfair, the Iranian people are suffering, and our (nuclear) activities are legal.

"These sanctions are illegal and only benefit Israel."

Western hopes

Western powers have indicated they are willing to engage with the new Iranian president - who is seen as moderate compared with the other five contenders.

"If [Mr Rouhani] lives up to his obligations under the UN Security Council resolutions to come clean on this illicit nuclear programme, he will find a partner in us," White House Chief of Staff Denis McDonough told CBS News.

EU foreign policy chief Catherine Ashton expressed hopes for a "swift diplomatic solution" to the Iranian nuclear issue.

Russia on Sunday congratulated Mr Rouhani on his victory. President Vladimir Putin "expressed confidence Hassan Rouhani's work will... further strengthen Russian-Iranian relations", said the Kremlin.

Tens of thousands of Iranians took to the streets after the results were announced on Saturday, many wearing Mr Rouhani's election colour of purple, but others dressed in the green of the reformist movement.

Mr Rouhani has already begun discussions on his cabinet with Ali Larijani, speaker for Iran's parliament, reported Iran's semi-official Isna news agency.

Parliament must approve his selections when he takes office in August.