By Marja Novak

LJUBLJANA (Reuters) - The European bail-in rules for banks in trouble do not increase the risk of contagion, Elke Koenig, chair of the Single Resolution Board, Europe's newest bank regulatory agency, told Reuters on Thursday.

She rejected a recent call from Bank of Italy Governor Ignazio Visco for the EU to backtrack on new bail-in rules on the grounds that they may mean the authorities are unable to prevent a contagion effect in a crisis.

"To put the entire system into question would ... take away the safeguard and not add to stability," Koenig said on the sidelines of a banking conference in Slovenia.

Asked whether the bail-in rules would make the possibility of contagion in a country more likely, she said: "No, I don't think that that is true."

She also said the issue of cases in which banks should not be allowed to pay bonuses, dividends and bond coupons was still being discussed.

"One lesson learnt is capital requirements should be transparent and bondholders have to know ... how close they are to the risk," Koenig said.

"I personally would always be by far harsher on dividends than I would be on bond interest, and I would be harsher on subordinated bond than on senior bond just because it's the normal credit hierarchy."

She said she did not see a need to impose new capital requirements on banks that would fail cyber-security stress tests.

"I find it fairly difficult to produce capital requirements or very specific scenarios," said Koenig.

(Editing by Hugh Lawson)