The US has vowed to continue nuclear negotiations after hardliner Ebrahim Raisi won the Iranian presidential election with a big margin.

State Department said indirect talks in Vienna between the US and Iran had made “meaningful progress” and that Washington wanted to build on this.

The State Department said Saturday it regretted Iranians were not able to participate in a "free and fair electoral process" in the country's presidential election.

In the first reaction from Washington to ultraconservative cleric Ebrahim Raisi's election win, a State Department spokesperson said "Iranians were denied their right to choose their own leaders in a free and fair electoral process."

The United States will nonetheless continue indirect talks with Iran on the US rejoining the 2015 nuclear accord that Donald Trump abandoned, the spokesperson also said.

Celebrations in Tehran.

In Iran's election, many political heavyweights were barred from running. Raisi is seen as close to 81-year-old supreme leader Ayatollah Ali Khamenei, who holds ultimate political power in Iran.

Many voters chose to stay away after the field of some 600 hopefuls, including 40 women, had been winnowed down to seven candidates, all men, excluding an ex-president and a former parliament speaker.

Three of the vetted candidates dropped out two days before Friday's vote.

On the Iran nuclear accord, the State Department spokesperson said indirect talks in Vienna between the US and Iran had made "meaningful progress" and that Washington wanted to build on this.

"We will continue discussions along with our allies and partners on a mutual return to compliance with the Joint Comprehensive Plan of Action," the spokesperson said.

The discussions in Vienna, brokered by European diplomats, have been locked in dispute on which sanctions imposed on Iran would be lifted.

Differing reactions
Ebrahim Raisi's victory on Saturday in a presidential election drew starkly opposed reactions, with Russia hailing a sign of greater regional stability but some condemning it as a farce.

- United States -
A State Department spokesperson said the United States regretted Iranians had been denied the chance to vote in a fair election. "Iranians were denied their right to choose their own leaders in a free and fair electoral process," said the spokesperson.

- Israel -
Foreign ministry spokesman Lior Haiat said on Twitter that Iran has "elected its most extremist president to date". Haiat called Raisi "the butcher of Tehran" who "has been rightly denounced by the international community for his direct role in the extrajudicial executions of over 30,000 people".

Raisi was "committed to Iran's rapidly advancing military nuclear programme, his election makes clear Iran's true malign intentions, and should prompt grave concern among the international community".

- Russia -
"Relations between our countries have been traditionally friendly," Russian President Vladimir Putin said in a message, saying Raisi's election would help develop "constructive bilateral cooperation in many fields and our partnership in international affairs".

"This responds entirely to the interests of the Russian and Iranian people and goes towards reinforcing regional stability and security," he said.

- Syria -
President Bashir al-Assad sent his "warmest congratulations" and wished Raisi "success in his new responsibilities ... and steering the country in the face of external pressure".

- Hamas -
Hamas spokesman Hazem Qassem said the Palestinian Islamist movement "congratulates" Raisi, adding: "Iran has always been a main, strong and real supporter of the Palestinian resistance and our national cause."

- Turkey -
Turkish President Recep Tayyip Erdogan congratulated Raisi, expressing the hope it would be beneficial for the Iranian people.

Erdogan said he believed "cooperation between our two countries would be strengthened further" and added that he was ready to work with Raisi.

- Iranian opposition -
Exiled opposition groups hailed what they termed a "boycott" of the presidential polls, where turnout was 48.8 percent.

Maryam Rajavi, the leader of the National Council of Resistance of Iran (NCRI), said the "unprecedented nationwide boycott" had signalled that Iranians had "voted for overthrow of the ruling theocracy".

The NCRI, in accusations backed by leading human rights groups, says Raisi was part of a commission that sent thousands of jailed opponents to their deaths within a few months in the summer of 1988.

"There is no longer any justification for the international community to deal with, engage, or appease a regime whose president is a notorious criminal against humanity," said Rajavi.

- Gulf and Yemen -
The rulers of the Gulf states of Kuwait, Oman, Qatar and the United Arab Emirates all sent congratulatory messages to Raisi, their state news agencies announced.

The senior political leader for Yemen's Tehran-backed Huthi rebels, Mahdi al-Mashat, also congratulated Raisi.

"The success of these elections in the Islamic republic of Iran is a victory for the Islamic revolution and solidifies the opposition to the American Zionist project," he said.

- Amnesty International -
"That Ebrahim Raisi has risen to the presidency instead of being investigated for the crimes against humanity of murder, enforced disappearance and torture, is a grim reminder that impunity reigns supreme in Iran," Amnesty said.

It called on the UN Human Rights Council's member states to take "concrete steps to address the crisis of systematic impunity in Iran".

Amnesty said they should establish "an impartial mechanism to collect and analyse evidence of the most serious crimes under international law committed in Iran to facilitate fair and independent criminal proceedings".