TEHRAN — Iran’s new President Hassan Rouhani on Sunday hailed his presidential election win as a victory over “extremism” as jubilant supporters took to the streets, pinning their hopes on an easing of Western sanctions.

Major powers quickly offered to engage with the moderate cleric and former nuclear negotiator, who has promised a more constructive approach to talks.

But Israel called for no let-up in the sanctions crippling the Iranian economy.

Iran’s reformist press hailed Rouhani as the “sheikh of hope” and said his victory promised a return to optimism after the eight-year grip of conservatives under outgoing President Mahmoud Ahmadinejad.

Tens of thousands of celebrators thronged the streets of Tehran, toting pictures of 64-year-old Rouhani and chanting pro-reform slogans as news of his victory spread on Saturday night.

“Tonight we rejoice as there is once more hope in Iran,” said Ashkan, 31, holding a poster of Rouhani and wearing a green wristband.

Rouhani was declared outright winner with 50.68 per cent of votes cast in Friday’s election.

In his first statement, he called on world powers to treat Iran with respect and recognise its rights, an apparent allusion to its controversial nuclear programme.

“This is a victory of intelligence, of moderation, of progress... over extremism,” Rouhani said.

“The nations who tout democracy and open dialogue should speak to the Iranian people with respect and recognise the rights of the Islamic republic.”

Then they will “hear an appropriate response”, added Rouhani, who has championed a more constructive engagement with world powers.

He won outright against five conservative candidates with 18.6 million votes out of the 36.7 million people who voted from an electorate of 50.5 million, the interior ministry said.

That was enough to ensure there would be no run-off against Tehran Mayor Mohammad Baqer Qalibaf, who came a distant second with 16.55 per cent.

Supreme leader Ayatollah Ali Khamenei, who has the final say in all strategic matters in Iran, including nuclear policy, congratulated Rouhani.

“I urge everyone to help the president-elect and his colleagues in the government, as he is the president of the whole nation,” Khamenei said on his website.

Reformist daily Etemad headlined: “A salute to Iran and to the sheikh of hope,” above a picture of a smiling Rouhani flashing a V-for-victory sign.

World powers expressed readiness to take up Rouhani’s offer of engagement.

The White House said it was prepared to engage Tehran directly to try to reach a “diplomatic solution that will fully address the international community’s concerns about Iran’s nuclear programme”.

Rouhani said in his campaign that he was ready to hold bilateral talks with Washington on Tehran’s nuclear programme.

He has also offered to restore diplomatic ties with the United States, which cut relations in the aftermath of the 1979 seizure of the American embassy by Islamist students.

“If he is interested in... mending Iran’s relations with the rest of the world, there’s an opportunity to do that,” White House Chief-of-Staff Denis McDonough told CBS News.

EU foreign policy chief Catherine Ashton, who acts as chief negotiator for the six powers involved in nuclear talks, said she was committed to working with Rouhani to find a “swift diplomatic solution”.

The Lebanese Shiite movement Hizbollah, a close ally of Tehran, called Rouhani a “beacon of hope”, while Syria said it will seek to expand its relations with its regional ally after his victory.

But Iran’s arch-foe Israel urged the international community to keep up its pressure on Tehran.

“The international community should not fall into wishful thinking and be tempted to ease pressure on Iran to stop its nuclear programme,” said Israeli Prime Minister Benjamin Netanyahu.

Israel, the region’s sole if undeclared nuclear power, has not ruled out a military strike to prevent Iran developing a rival arsenal.

Iran insists it has no such ambition and that its nuclear programme is for peaceful power generation and medical purposes only.

King Abdullah of regional powerhouse Saudi Arabia was among Gulf Arab states to congratulate Rouhani.

The Brussels-based International Crisis Group’s senior analyst on Iran said: “Rouhani cannot change the core of Iran’s nuclear strategy, which is determined by the supreme leader,” Khamenei.

“But what he can alter is the tone and the team,” while easing Tehran’s isolation which could lead to an easting of sanctions, Ali Vaez said.

Rouhani inherits an economy that has been badly hit by EU and US sanctions targeting the key oil and banking sectors.

Inflation has climbed to more than 30 per cent, as the rial has lost nearly 70 per cent of its value against the dollar, sending the cost of imported goods soaring and slashing the purchasing power of ordinary people.

Rouhani has pledged to tackle the problems by taking a more constructive approach with the major powers that might lead to the sanctions being relaxed.

Friday’s vote was the first since the controversial 2009 reelection of Ahmadinejad triggered mass protests that were crushed with deadly force.