MILAN, June 13 (Reuters) - Shares in Italian banks slid further on Monday, after a plunge on Friday, as investors fretted about their exposure to Italian government debt, with the risk premium Rome must offer on its bonds over safer German debt hitting a two-year high.

The gap between Italian and German bond yields hit the highest since May 2020 on Monday after the European Central Bank last week flagged an interest rate hike in July without also unveiling support for so-called periphery euro zone bonds, such as Italian debt.

The policy shift has rekindled fears that more indebted southern European countries such as Italy will struggle to adjust to tighter financing conditions, in a blow to their already fragile economies and their banks' balance sheets.

"Sovereign spreads are yet again at centre of investors' debate for periphery banks, following rising yields/spreads," Citi analysts said on Monday.

At 0718 GMT, Italy's banking index was down 3.6%, having lost a quarter of its value since the start of the year. Shares in Italy's biggest bank Intesa Sanpaolo were down 4%, and UniCredit's were down 3.6%.

BPER Banca, which on Friday presented a new business plan bracing for higher bad loans and cost inflation, lost 5.5%, triggering an automatic trading suspension. BPER had closed down 13% on Friday, when Italy's banking index fell 8.5%.

Higher sovereign debt costs inflate costs for banks raising capital on debt and equity markets. Their loan books are also at risk if borrowers struggle with rising interest payments.

However, since the sovereign debt crisis of 2011-2012, banks have taken action to limit the impact on capital of falling prices for their sovereign bond holdings.

"Both Spanish and Italian banks improved significantly vs. the past their overall capital, asset quality and liquidity position, and profitability has high gearing to rising rates," Citi said.

Citi said it remained positive on Italian and Spanish banks, though sovereign risks could weigh on shares, overshadowing fundamentals.

"Any potential announcement from ECB to mitigate/control government bond yields in periphery would be positive for banks' shares, but might not materialize very quickly."

Sources have told Reuters a large majority of ECB policymakers see no need for now to announce new bond purchases to rein in spreads between core and peripheral bond yields as borrowing costs remain low. (Reporting by Valentina Za Editing by Mark Potter)