Italy's bank shares have plunged, shaking the financial foundations of the euro zone's third-largest economy and threatening contagion to other EU nations.

The crisis could push Italy back into recession and, in a doomsday scenario, generate a Greece-type meltdown that Europe would find almost impossible to contain

Italy's banks are suffocating under a pile of non-performing loans and, adding to the growing sense of instability, Prime Minister Matteo Renzi has promised to resign if he loses a referendum in October on constitutional reform.

Recent opinion polls say he will fall well short.

"Italy faces a severe crisis that is exponential. This is not gradual and not linear," said Francesco Galietti, head ofthe Policy Sonar risk consultancy and a former finance ministry official. "The immediate trigger is the banking crisis."

Italy's bank sector index has fallen 30% since Britain voted on 23 June to quit the European Union, bringing its losses so far this year to 57%. The euro zone banking stocks index has dropped 22% and 37% respectively.

Today the Italian index lost a further 1.44% to trade around three-year lows.

Italy is politically and financially fragile, often described as "too big to save" in a crisis, so even though there is very little direct economic linkage between its banks and the Brexit vote, any global shock creates major tremors here.

"Italy is essentially the fault line of Europe," said a former IMF official, speaking on condition of anonymity.

"Both the public debt and the banking sector are on a powder keg, being maintained by a process of non-recognition of accumulated losses in the system that they keep rolling over.The real problem is that somebody has to take the losses eventually."

Immediate concerns centre on Italy's third-largest lender,Banca Monte dei Paschi di Siena, which has the highest ratio of bad debts to outstanding loans among listed Italian banks. It has been told by the European Central Bank to slash these debts by 40% over three years.

Rome is in talks with Brussels to devise a plan to recapitalise its lenders, including BMPS, hoping to use publicmoney to stave off potentially huge losses for bank bond and shareholders - many of them ordinary retail investors.

Such a deal might require the bending of anti-bailout rules that the EU adopted in 2014 to force investors and some depositors to share the burden of bank failures.

Germanysays the rules must be respected, but Italy says flexibility is needed to prevent possible bank contagion stemming from Brexit.

"A solution should be found quickly or the world's oldest bank could fail and bring down the rest of Europe's embattled banking sector with it. The EU needs to show flexibility or Italy could go under," said Andrew Edwards, CEO of British based financial company ETX Capital.

Highlighting these concerns, BMPS dropped 20% today, bringing its losses this year to almost 80%.

One EU official told Reuters that on Monday night at a meeting of the Eurogroup Working Group, the body that preparesthe meetings of euro zone finance ministers, national envoys had expressed "concern" for the situation in Italy.

However, a second EU official said there was little appetite to change or soften the bail-in rules, with opponents arguing that Italy had signed up to the rules so should abide by them.