Informal opinion polls show the former president, once considered a racing certainty to sweep home in Friday's vote, is facing a twin challenge from Mohammad Baqer Qalibaf and Mostafa Moin.
Increasing indications suggest that none of the eight candidates will poll the 50% needed to win outright, pushing the vote into an even more unpredictable second round run-off, the first in the history of the Islamic republic.
However the unscientific nature of the polls makes the outcome of Friday's vote impossible to call and a surprise similar to outgoing President Mohammad Khatami's shock 1997 landslide win cannot be ruled out.
Supporters of Moin have been expressing confidence that their man could spring such a surprise, despite calls from some liberals to boycott the vote and the disappointment over the unfulfilled promises of Khatami's difficult presidency.
"If we have two more weeks, without any doubt, Moin can win the elections. Moin will be for sure in the second round. It's possible he can win in the first round," said Mohammad Reza Khatami, brother of the current president.
Qalibaf, a former police chief, has been making efforts to increase his appeal and is also expressing confidence of a strong result.
Moin is presenting himself as
the reformist candidate
The remaining candidates -Mohsen Rezai, Tehran mayor Mahmoud Ahmadinejad, former state television boss Ali Larijani and Mohsen Mehr-Alizadeh and Mehdi Karoubi - are expected to take a smaller share of the vote.
With less than 24 hours of allowed campaigning time remaining, activists were hard at work in Tehran pasting up posters of their candidates in what has been arguably the most vibrant election in the history of the Islamic Republic.
Seeking to present a human and caring face to the electorate, Rafsanjani broadcast an election film in which the cleric was seen having his well-kept silver hair cut at the barbers, watching football and taking off his turban.
Even the most conservative candidates have gone out of their way to court Iran's increasingly youthful population with a combination of slick marketing and a conspicuous avoidance of heavy duty ideology.
There has been an unprecedented cut-and-thrust in the political debate, with crucial issues such as renewing relations with the United States and personal liberties debated openly and not swept under the carpet.
"It seems that the US is choosing a new approach but it needs to do more"
Also new has been the large amount of funding flowing into candidates' campaign coffers - criticised in some quarters as un-Islamic - allowing them to put up posters all over the country and staging large-scale election rallies.
High participation is also important to bolster the legitimacy of the authorities, who slammed a string of deadly pre-election blasts that killed up to 10 people on Sunday they feared might lessen the turnout.
New era relations
Courting public opinion in the West, Rafsanjani also gave a live interview to a US news network in which he said a new chapter in relations with arch-foe the United States would be possible if he won the presidency.
But he also made clear his view Iran had done enough to show its goodwill and it was up to the United States to make a move that would thaw relations frozen for more than a quarter of a century.
"It seems that the US is choosing a new approach but it needs to do more," the former president told CNN.