Struggling Italian banks took a hammering on the Milan stock market Monday as the European Central Bank demanded action over the high level of bad loans at the country's number-three lender.

Burdened by fragile balance sheets and a staggering 360 billion euros ($401 billion) in bad loans, the Italian banking system is emerging as a big worry for bank investors, already shaken by Britain's June 23 vote to leave the European Union.

Italian Prime Minister Matteo Renzi's government is in talks with the European Union over how to shore up ailing banks but its task is complicated by EU rules that bar the use of public money to do so.

Shares in Banca Monte dei Paschi di Siena, or BMPS, plummeted 14.0 percent to close at 0.29 euros as investors fretted over its gross bad loans, which amount to 46.9 billion euros.

Other Italian banks also fell heavily, with top bank Unicredit declining 3.6 percent and others down by similar or larger margins.

Since January, the FTSE Italia All-Share Banks index has plunged 55 percent.

In a draft letter to BMPS, the Frankfurt-based ECB told the bank to lower its gross bad loans by more than 13 billion euros to a maximum 32.6 billion euros in 2018, the Italian bank said in a statement.

- Deep concerns -

The central bank also ordered BMPS to present by October 3 its plans to cut the ratio of doubtful loans to 20 percent of the total loan portfolio in 2018.

BMPS said the ECB requirements were in line with plans that the Italian bank had already approved.

Those plans, which focused on a faster process of ridding itself of bad loans, had been submitted at the time for the ECB to assess, the bank said.

"The bank has immediately initiated discussions with the European Central Bank in order to understand all the indications included in this 'draft' letter, and to present its reasoning before the final decision expected by the end of July 2016," BMPS said.

Market concerns have deepened ahead of the July 29 publication of European Banking Authority stress test results, which may reveal shortfalls in Italian banks' capital.

Saxo bank economic analyst Christopher Dembik said there is a "strong chance" that Italian banks will run into trouble in the stress tests as most of them have bad loans amounting to more than 10 percent of the total.

- Bail out talks -

Last week, the European Commission agreed to allow the Italian government to offer government guarantees as a form of short-term liquidity for solvent banks, with a reported total of up to 150 billion euros.

Italian media say Rome is seeking a six-month suspension or relaxation of EU rules that require investors to pay the cost of rescuing a troubled bank before public funds are used for a bail-out.

Citing officials and bankers, the Financial Times said Monday that Italy could defy the EU and use public money if the banking system came under "severe systemic distress".

A government official told AFP that the prime minister had repeatedly stressed his desire to defend savers, preferring to use "market solutions in line with European rules".

German Chancellor Angela Merkel last week warned that it was not possible to change the rules "every two years" while Brussels argues that Italy has other solutions available that respect EU regulations.

Renzi has raised the possibility of boosting the finances of Atlante, a fund created by financial institutions to help fragile banks.

As if the Italian investors were not already sufficiently stressed, the climate is further clouded by the government's plans to hold a referendum in October to reform the constitution.