Speaking alongside French President Emmanuel Macron, she said: “We are also ready to create a joint deposit insurance system in perhaps not the immediate, but more distant future.
“We do want liability and risks to be kept together.”
Mrs Merkel stressed she was “very optimistic” that the banking union, involving the transfer of banking policy from the national to the EU level in several member states, could be completed.
But behind the scenes, there is ongoing debate about how far bad loans from banks need to be reduced before European solidarity can be applied to financial institutions in need.
Mrs Merkel, who agreed to the banking union in March, said she wants to see a further reduction of the debts and risks of national banks in the EU states.
At the time she said Germany had always been willing to give up sovereignty, if things could be better regulated by Europe.
Her country was also willing to help stabilise the Euro and was prepared for joint euro debt, she added.
The reduction of bad loans is progressing slowly in Europe.
Italy reported the sale of billions of financial investors before its general election in March – but this represents just a fraction of the total of bad loans.
German banks are feeling the pressure, with NordLB working hard to solve its capital problem after the takeover of the ailing Bremer Landesbank.
Mrs Merkel and Mr Macron said the EU should accept a comprehensive “package of reforms” in June in areas such as the euro-monetary union and asylum and foreign policy.
The possibility of an EU-wide finance minister, and a Eurozone budget have also been floated.
She added: ”We agree that the Eurozone is not yet sufficiently crisis-proof.
“We bring in some other aspects, but I believe that the sum of our proposals will lead to a good result at the end.”
The pair insisted that by June, they wanted to develop a common position.