Four candidates are still in contention, but analysts see incumbent President Hassan Rouhani and challenger Ebrahim Raisi as the favourites. The survey was conducted after the first two presidential debates, held in April and May.
The president has faced a significant challenge from conservatives because the landmark nuclear deal with world powers that he negotiated in 2015 has not triggered the economic recovery he predicted. The deal saw Iran limit its enrichment of uranium in exchange for the lifting of some economic sanctions. A Rouhani win could signal that Iran would stick with its end of the nuclear deal, while a conservative candidate could disrupt the agreement.
The two adopted similar campaign tactics, criticizing Rouhani's economic record - particularly high unemployment, which rose 1.4 percent past year to 12.4 percent - and his policy of detente with the West.
That has led to speculation that Iran's next government will engage less with the West, especially after Khamenei called on whoever wins to avoid relying on foreign investors to strengthen the economy - a comment widely interpreted as a criticism of Rouhani. Rouhani won just over 50 percent, averting a second round. Many residents of Iran's capital vented anger at Qalibaf and Tehran authorities after a massive January fire at a historic high-rise caused the building to collapse, killing 26 people, including 16 firefighters.More news: Trump Promises Israel-Palestine Peace, But Offers No New Policies
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"It is my belief that Iranian ethnic and religious groups can play an equal role in the development and progress of the country", the presidential hopeful said, adding that their talents should be utilized in the country's management.
Last week, Khamenei maintained his drumbeat of disapproval of Rouhani, dismissing the idea that war with the West had been averted by the nuclear diplomacy and dismissing a United Nations education program endorsed by the Rouhani administration promoting gender equality and life-long learning opportunities. Undoubtedly, with Mr. Trump, the Iranian hardliners have tried to capitalise their power while seeking to reunite under one consensus standard-bearer - none other than Ebrahim Raisi. He was deputy head of the judiciary for 10 years before being appointed in 2014 as Iran's prosecutor-general.
Raisi is a conservative cleric, a close ally of Supreme Leader Ayatollah Ali Khamenei, and the custodian of both the wealthiest charitable foundation in Iran and the Muslim world, Astan Quds Razavi, and the Imam Reza shrine.
"I ask my supporters throughout the country to use all of their potential" to elect Raisi, Ghalibaf said in a statement carried by state media. Khamenei's manipulation of the Iranian elections exposes the fact that they are a sham and a scandal.