Prime Minister Matteo Renzi's decision to quit followed voters' rejection of his constitutional reform plans in a referendum and it has raised questions about the country's stability and especially about the ability of some of its ailing banks to raise capital.

Asked at a European Parliament committee hearing about the state of Italian banks, SRB head Elke Koenig said: "There was a political referendum. The banks are, the markets are fairly calm today and I would not immediately link that to our day-to-day business."

Answering another question about Italian banks bolstering their capital base, Koenig indicated she would see an injection of capital by the state as a poorer option than private funding. She said she always hoped banks would find "private solutions".

Koenig said it would take time to solve problems at some Italian banks. On Monday Banca Monte dei Paschi postponed its plan to raise 5 billion euros after the Italian referendum, sources said.

If private solutions are no longer available, Koenig said EU rules are clear and require losses for bank creditors if lenders receive public support, the so-called 'bail-in'. "There is no way around the rules," Koenig said.

The SRB is the body that oversees euro zone banks' orderly liquidations. It has drafted "resolution plans" for all the currency bloc's major lenders.

Monitoring of Italian banks has increased after the referendum, EU sources said, but no resolution measure is on the cards at the moment.

(Reporting by Alastair Macdonald and Francesco Guarascio; Editing by Gareth Jones)