* Bulgaria to be first non-euro zone bank to join mechanism
* No political consensus on rescue package for Corpbank
* ECB says not been contacted formally by Bulgaria
* Political parties wrangle over safeguarding deposits
* Prosecutors amend charges against four Corpbank officials (Adds comments by ECB, government, analyst, adds details, background)
SOFIA, July 15 (Reuters) - Bulgaria's central bank has begun talks with the European Banking Authority about conducting a review of the quality of its banking supervision, it said on Tuesday, following runs on two lenders in June.
The Bulgarian National Bank has also been in touch with the European Central Bank (ECB) about joining the European Single Supervisory Mechanism (SSM), it said in a statement.
Bulgaria would be the first country outside the 18-nation euro zone to join the Single Supervisory Mechanism, set up in response to the global financial and euro zone debt crises, though neighbouring Romania has said it could apply for membership next year.
Bulgarian President Rosen Plevneliev announced Sofia's intention to join the European supervision scheme on Monday, as the government grapples with the fallout of the country's worst financial crisis since a number of bank collapses in the 1990s.
There is still no agreement on a deal between the ruling coalition and the opposition about the terms of a rescue package after a run on deposits at Corporate Commercial Bank (Corpbank) , Bulgaria's No. 4 lender, in June.
The run on Corpbank and the subsequent hit on another lender raised questions about the quality of banking supervision in the Balkan state, which joined the European Union in 2007 and is its poorest member.
"It is a very good idea to join Europe's banking union," said Georgi Ganev, a lecturer on banking at Sofia University.
"Because of the total collapse of trust in state institutions, any solution that increases this trust is welcome. There is a high level of confidence in EU supervisors."
A source familiar with the process said any application would take several months and could not be processed in time for Bulgaria's banks to undergo the landmark review of euro zone lenders that the ECB is carrying out this year.
If the application proceeds, Bulgaria's banks would go through a similarly robust analysis before the ECB takes over their supervision.
"We have taken note of the statements made by the Bulgarian authorities. The ECB hasn't been contacted formally," an ECB spokesman said.
The central bank seized control of Corpbank following a run on the lender by depositors unnerved by reports of shady deals involving its main shareholder, Tsvetan Vassilev, and amid a public feud between Vassilev and a business rival.
Vassilev has denied any wrongdoing and said the run, during which more than a fifth of deposits were withdrawn, was a plot against him by his rivals.
The problems at Corpbank, where state companies kept a large part of their funds for years, have brought renewed scrutiny of Bulgaria, including the murky relations between the political elite and powerful businessmen.
The central bank, after talks with the government, has said it will let Corpbank collapse, transfer the good assets and liabilities to a recently acquired subsidiary, and initiate bankruptcy proceedings against the bank.
The plan requires a special law in parliament to be passed.
However, the delay in achieving a political consensus on the deal means that the planned reopening of the subsidiary, which would relaunch as a nationalized institution on July 21, could also be postponed until further notice.
Much of the wrangling has centred on whether the government can honour an earlier promise that depositors would not "lose a single lev" as a result of the crisis. The main opposition party GERB and even members of the ruling Socialist party have insisted the government guarantee deposits only up to 100,000 euros.
The government has said that deposits under 100,000 euros total 3.6 billion levs ($2.50 billion) in the bank, leaving about 1.5 billion levs unprotected - money that also includes deposits of state and private companies, and municipalities.
"The rescue package will ensure the normal work of dozens of Bulgarian companies and can minimise the overall loss for society from the halting of the operations of this relatively big Bulgarian bank," the government said in a statement on Tuesday.
It remains unclear what size of bailout will be required to prop up the subsidiary. The government may issue new debt, which could swell Bulgaria's fiscal deficit to 3 percent of gross domestic product, the finance minister has said, against a planned 1.8 percent for 2014.
Bulgarian prosecutors have charged four Corpbank officials with pilfering more than 200 million levs from the bank.
However, prosecutors on Monday tweaked their initial charges, which accused the officials of taking the money out in cash a day before the central bank took control. Instead, they said the funds were gradually embezzled since December 2011.
Two of them, chief cashier Margarita Petrova and the deputy chief accountant of the bank, will remain in custody. The chief accountant is under house arrest and Orlin Rusev, one of Corpbank's executives, was released on bail of 10,000 levs.
A lawyer for Petrova told Reuters her client will plead not guilty, adding the other three have also denied wrongdoing. The other officials could not immediately be reached.
"The situation with Corpbank sheds light on illegitimate links between politicians and businesses. The bank's case is seen as isolated as this bank had a special role - the intertwining of political and economic interests," said Daniel Smilov, a political analyst at the Centre for Liberal Strategies, a Sofia-based think tank.
"Bulgaria now has a chance to clean up and really prosecute all those who were responsible for the situation," he said. ($1 = 1.4376 Bulgarian levs) (Additional reporting by Laura Noonan in London, Angel Krasimirov in Sofia and Radu Marinas in Bucharest; Writing by Matthias Williams; Editing by Susan Fenton)