The US has said that it is prepared to engage Iran directly over its disputed nuclear programme after Hassan Rouhani was declared the country's new president.
The White House said on Saturday such engagement would be aimed at reaching a "diplomatic solution that will fully address the international community's concerns about Iran's nuclear programme".
Iran's president-elect earlier urged world powers to speak to his country with respect and acknowledge its rights in order to receive an appropriate response, as he hailed his election as a "victory of moderation over extremism".
"A new opportunity has been created by this great epic, and the nations who tout democracy and open dialogue should speak to the Iranian people with respect and recognise the rights of the Islamic Republic," Rouhani said.
While the West welcomed his conciliatory tones, Israel reacted to Rouhani's win by saying it was Supreme Leader Ayatollah Ali Khamenei who had so far decided on nuclear policy, not the president.
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"After the elections, Iran will continue to be judged by its actions, in the nuclear sphere as well as on the issue of terror," the foreign ministry said in a written statement after Rouhani was elected.
Prime Minister Benjamin Netanyahu urged continued international pressure on Iran to curb its nuclear programme after the election of a new president widely seen as a moderate.
"The international community must not give in to wishful thinking or temptation and loosen the pressure on Iran for it to stop its nuclear programme," Netanyahu told his cabinet, according to a statement released by the Prime Minister's Office.
Syria conflict concerns
Russian President Vladimir Putin congratulated Rouhani on his victory in Iran's presidential election and urged him to forge closer ties with Moscow.
"Putin expressed confidence that Hassan Rouhani's work on this high post will promote the flourishing of [Russian] friend Iran and further strengthen Russian-Iranian relations," the Kremlin quoted Putin as saying in a message to Iran's president-elect on Sunday.
Britain's Foreign Office called on Rouhani to take Iran on a different course and highlighted concerns about Iran's nuclear programme, its relationship with the international community and its human rights policy as areas where improvement was required.
France's Foreign Minister Laurent Fabius said the European nation was ready to work with Rouhani on issues ranging from Tehran's nuclear drive to the conflict in Syria.
The key opposition Syrian National Coalition umbrella grouping urged the president-elect to review his country's support for the Syrian government.
"The Syrian National Coalition believes that it is its duty to call on the new president of Iran to rectify the mistakes made by the Iranian leadership," the group said on Saturday, in reference to Tehran's staunch backing of Syrian President Bashar al-Assad.
Jack Straw, Britain's former foreign secretary who dealt with Rouhani during nuclear negotiations from 2003 to 2005, called Rouhani a "very experienced diplomat and politician" who was "tough but fair".
Lack of transparency
The West hopes that the former chief nuclear negotiator's concilatory statements will lead to talks on Iran's nuclear programme, which it suspects is aimed at building nuclear weapons. However, Iran insists it is for peaceful purposes like generating energy.
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EU foreign policy chief Catherine Ashton said on Saturday that she was committed to working with newly elected Iranian President Hassan Rouhani on finding a solution to Tehran's disputed nuclear programme.
The White House said in a written statement it respected the will of the Iranian people and congratulated them for taking part in the election, praising "their courage in making their voices heard."
It said the vote on Friday was held amid lack of transparency, censorship of the media, the Internet and text messages, and "an intimidating security environment that limited freedom of expression and assembly".
"However, despite these government obstacles and limitations, the Iranian people were determined to act to shape their future," it said.
"It is our hope that the Iranian government will heed the will of the Iranian people and make responsible choices that create a better future for all Iranians."
Gulf leaders react
Leaders of Gulf states, which have tense relations with Iran, have swifty welcomed moderate cleric Hassan Rouhani's election as the new president of the republic, several state news agencies said.
"We look forward to working together for the good of this region and the Emirati and Iranian peoples," the United Arab Emirates President Sheikh Khalifa bin Zayed al-Nahyan wrote in a telegram to Rouhani, state news agency WAM said late Saturday.
"We are keen to forge relations based on cooperation with the Islamic Republic of Iran," he added.
Leaders of Bahrain, Kuwait and Qatar also congratulated Rouhani, state news agencies in their respective countries said.
Saudi Arabia is yet to comment on his win.
The Sunni-ruled Gulf countries are wary of their Shia-dominated neighbour, mainly over its nuclear ambitions and allegedly supporting the Shia-led opposition in Bahrain, where demonstrations continue.
The UAE accuses Iran of occupying since 1971 three islands in the Gulf that the Arab nation claims to own under an agreement signed with colonial-era Britain before it withdrew from that part of the Gulf.