Euro zone banks should watch their sources of funding or they risk being "caught off guard" by rising interest rates, the European Central Bank's top banking supervisor Andrea Enria said on Tuesday.

Introducing the ECB's annual report on banking supervision, Enria said euro zone banks were solid but warned that a sharp rise in borrowing costs over the past year meant lenders could no longer rely on cheap funding and rising financial markets.

"Increasing interest rates and quantitative tightening require banks to sharpen their focus on liquidity and funding risks," said Enria, in remarks the ECB said were drafted in February, before recent turmoil in the global banking system.

"There is a risk that banks might be caught off guard," he warned.

The global financial system is on tenterhooks after two large banks - Silicon Valley Bank of the United States and Switzerland's Credit Suisse - ran out of cash, albeit for different reasons.

Enria's report warns banks about a likely hit to their net worth as borrowing costs rise.

This was a major problem at SVB, which had invested customer deposits without hedging itself against the risk of rising rates, ultimately suffering a bank run.

"(Banks) should adopt sound and prudent asset and liability management modelling practices in order to capture shifts in consumer preferences and behaviour when interest rate regimes change," Enria said. "They should also carefully monitor risks arising from hedging derivatives."

Credit Suisse also suffered massive deposit outflows, especially from its international business, after a string of scandals.

Large euro zone banks had a leverage ratio - a broad gauge of their solidity in which capital is measured as a percentage of total assets - of 5.2% on average as of September 2022, the report showed.

This one of the lowest levels since the ECB started supervising them in 2014 but still well above requirements, the ECB said in the report.

Enria is due to appear before the European Parliament at 1330 GMT on Tuesday and may give updated figures about the health of the euro zone's banking system. (Reporting by Francesco Canepa; Editing by Catherine Evans)