Story highlights President Mahmoud Ahmadinejad is term-limited and can't run again

His top aide is one of the candidates

Ex-president and Ahmadinejad critic Akbar Hashemi Rafsanjani also registered to run

The Guardian Council vets candidates and decides who can run

Hundreds of candidates are vying to become Iran's next president, with hopefuls ranging from friends to foes of current President Mahmoud Ahmadinejad.

A total of 686 candidates have registered for the June election, Iran's state-run Press TV reported.

Ahmadinejad is term-limited and cannot run for a third straight term.

But other big names are in the mix, including Ahmadinejad's top aide Esfandiar Rahim Mashaei and former Iranian President Akbar Hashemi Rafsanjani.

Ahmadinejad has been grooming Mashaei to take over for years, and the two are like-minded in their nationalism and shared disdain for the clerical establishment, according to Geneive Abdo , a fellow at the Stimson Center's Middle East Program and a nonresident fellow at the Brookings Institution.

But the Guardian Council, which is controlled by Supreme Leader Ayatollah Ali Khamenei, vets candidates and decides who is allowed to run for president, Abdo said. She said the council is not expected to allow anyone from the so-called "deviant faction" of Ahmadinejad's supporters to run.

JUST WATCHED Clerics angry Ahmadinejad hugged woman Replay More Videos ... MUST WATCH Clerics angry Ahmadinejad hugged woman 01:35

JUST WATCHED Ahmadinejad on the West bluffing Replay More Videos ... MUST WATCH Ahmadinejad on the West bluffing 01:25

Rafsanjani, on the other hand, has long been a staunch critic and bitter political rival of Ahmadinejad's. He served two terms as president from 1989 to 1997.

Weeks after the 2009 elections, Rafsanjani condemned the regime's violent crackdown against the opposition movement and spoke out for the people's right to peacefully protest.

He later toned down the attacks and made statements of apparent support of the regime and the supreme leader, Khamenei.