NICOSIA, Cyprus--Cyprus's president has accused the island's central bank chief of bowing to political pressure when he failed to prevent a looming banking crisis that led to the collapse of the country's second-biggest bank last month.

The charges, made in a letter sent to European Central Bank head Mario Draghi, represent the latest salvo in the deepening rift between President Nicos Anastasiades and Central Bank of Cyprus Governor Panicos Demetriades over who is to blame for the country's financial crisis.

The letter comes after three members of the central bank's board resigned last week to protest the bank chief's handling of the country's financial crisis and a week after Cyprus's president fired Mr. Demetriades's deputy. As the same time, lawmakers in Cyprus are considering an investigation into whether the central bank chief misled the parliament over events relating to the crisis.

Amid the fray, Mr. Draghi last week warned Cyprus's government that any move to undercut the autonomy of its central bank -- which enjoys political independence --could lead to a legal challenge at the European Court of Justice.

In the letter to Mr. Draghi dated April 15, Mr. Anastasiades said that the embattled central banker's decision to continue extending emergency credit to Cyprus Popular Bank PCL (CPB.CP)--after the bank known as Laiki was clearly insolvent from June of last year according to Mr. Anastasiades--violated Mr. Demetriades' duties as governor and demonstrated shortcomings in regulating and supervising the island's banks.

Mr. Anastasiades also cited in the six-page letter, seen by The Wall Street Journal, public comments by Mr. Demetriades that the central bank's aim was to prevent Laiki's collapse before this year's presidential elections, when Mr. Anastasiades's predecessor's term ended. The current Cypriot president said the comment "raises questions" about the central bank governor's independence from the former government.

Mr. Demetriades, who was appointed last year by outgoing President Demetris Christofias, was not immediately available for comment.

The central banker has previously said he would not step down and, in a recent media interview, said that the central bank's independence was under attack. As part of the ECB's network or euro-zone central banks, Mr. Demetriades cannot be removed from office except in the case of serious crimes or an inability to perform his functions as governor.

An ECB representative confirmed that the ECB has received the letter from the Cypriot president, but declined to comment on the content.

The letter also appears support one of the allegations made by lawmakers seeking a probe into Mr. Demetriades. They have accused him of trying to sidestep an independent audit of what went wrong at Laiki. "In my opinion, Governor Demetriades, for his own reasons, clearly failed or omitted to properly instruct [audit firm Alvarez & Marsal] to carry out a full inquiry, especially for Laiki Bank, which, as he had stated was insolvent," the letter added.

Faced with the imminent collapse of its financial sector, Cyprus this month agreed to some 13 billion euros ($17 billion) worth of measures -- more than initially expected -- to fix its public finances and restructure its two biggest banks in exchange for a EUR10 billion loan from its euro-zone peers and the International Monetary Fund. The bailout has resulted in uninsured deposits over 100,000 euros being largely wiped out at the two biggest banks--Laiki and Bank of Cyprus (BOCY.CP).

The austerity measures, combined with the effects of the banking crisis and capital controls put in place to stem a feared bank run, are expected to push Cyprus deep into recession this year.

Christopher Lawton in Frankfurt contributed to this story

-Write to Philip Pangalos at philip.pangalos@dowjones.com

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