* Major Iranian bank bosses lose their posts -ministry
* $2.6 bln financial fraud has shaken Ahmadinejad government
* Economy Minister faces impeachment threat by lawmakers
TEHRAN, Sept 27 (Reuters) - A $2.6 billion financial fraud that has shaken the government of Iranian President Mahmoud Ahmadinejad saw the heads of three of the country's banks ousted on Tuesday as lawmakers threaten to impeach the economy minister.
The biggest fraud in the 32-year history of the Islamic Republic could result in the death penalty for anyone found guilty of it and has become part of an increasingly ugly split in the conservative elite that runs Iran.
Ahmadinejad has rejected claims from his hardline rivals that the investment company at the centre of the scandal has links to his key aide, Esfandiar Rahim Mashaie, the focus of fierce criticism by conservative politicians and clerics.
But that has not satisfied members of parliament who have already threatened to impeach the president over other issues and critics who accuse him of being in the thrall of a "deviant current" of advisors seeking to undermine the authority of Supreme Leader Ayatollah Ali Khamenei.
With the government seeking to assert its authority in the case, an ad hoc governmental committee has instructed the Central Bank of Iran to remove the head of the bank at the centre of the allegations, Bank Saderat, and of the smaller Bank Saman, the Economy Ministry said on its website.
The chief of state-owned Bank Melli, Iran's biggest bank, handed his resignation to the Economy Ministry, the website said.
A spokesman for Bank Saderat -- a large, partly privatised company -- denied reports that the bank's chief had lost his post, while Bank Melli and Bank Saman were not immediately available for comment.
At least 19 people have been arrested so far for the alleged scam which the judiciary said involved the fraudulent opening of bank letters of credit by the Amir Mansour Aria investment group.
Hardline conservative newspaper Kayhan has said the mastermind behind the fraud had links with Ahmadinejad's closest aide.
Mashaie, once talked about as a possible successor to Ahmadinejad whose time in office ends in 2013, has been accused of heading the "deviant current" which the president's foes say intends to dilute Iran's Islamic character and undermine the role of the clergy.
The financial scandal has erupted in the run-up to parliamentary elections in March and is set to become a central issue.
With Iran's reformists sidelined after the government crushed huge demonstrations following Ahmadinejad's disputed re-election in 2009, the March vote will largely be fought between rival conservative factions.
Prosecutor General Gholamhossein Mohseni-Ejei has said culprits of the fraud may be executed.
"The perpetrator of the recent embezzlement will be hanged if proven beyond doubt to be 'corrupt on Earth'," he said, referring to a crime that carries the death penalty under Iran's version of Sharia law.
Upping the pressure on Ahmadinejad, twenty members of Iran's parliament have signed a petition to impeach Economy Minister Shamseddin Hosseini over the affair.
"People who have given 200,000 martyrs for this establishment do not expect to witness from it such a grand violation of its banking system that has aroused a public distrust of the system," lawmaker Aziz Akbarian told the semi-official Fars news agency. (Additional reporting by Hossein Jaseb; Editing by Alexander Smith and Hans-Juergen Peters)