Ahmadinejad economic policies have concerned some at home, while on the international stage he has earned notoriety for his comments on Israel and his refusal to concede to Western demands over Iran's nuclear programme.
Rezai, who says he is standing as an independent, has accused Ahmadinejad of pushing Iran to the edge of a "precipice", while Mousavi has vowed to change the "extremist" image Iran has earned abroad under its current president.
For his part, Karroubi, the most overtly reformist of the four, insists he will be careful while introducing changes not to antagonise the country's political conservatives.
But Ayatollah Ali Khamenei, Iran's supreme leader, appears to have come out in support of Ahmadinejad, urging voters not to elect a candidate who could adopt a pro-West stance.
It would be a "catastrophe" for Iran, Khamenei said, if a candidate who "thinks about endearing himself to some Western power or an international arrogant" is elected next month.
A total of 475 Iranians had registered as prospective candidates - 433 men and 42 women.
|Mousavi was Iran's last prime minister,
before the post was abolished [EPA]
All were screened by the 12-member Guardian Council, made up of six clerics selected by Khamenei and six jurists proposed by the head of the judiciary.
In the 2005 election, won by Ahmadinejad, eight candidates of the 1,014 who registered were approved, and eventually just seven stood.
Karroubi blamed "irregularities" for his defeat in 2005 and has demanded transparency this time round.
"It is not possible to have any irregularities in this election. Even if there are some minor infringements, the system is developed in such a way as to confront these," Mahsouli said.
He said a lottery would now be held to determine the order of televised debates by candidates.
Ezatollah Zarghami, the head of Iran's state-run television, said last week that the channel would air debates by candidates and vowed "fairness" in its coverage.
But Mousavi, Ahmadinejad's main rival, has accused state television of "repeated and open breaches of neutrality".
His comments were made in a letter to Ali Larijani, the parliament speaker; Ayatollah Mahmoud Hashemi Shahroudi, the head of the judiciary; and Ghorban Ali Dorri Najafabadi, Iran's attorney-general.
Karroubi has also previously accused television of broadcasting biased coverage in favour of Ahmadinejad.