The European Central Bank vowed to support euro zone banks with loans if needed, adding the Swiss rescue of Credit Suisse was "instrumental" in restoring calm.
There are also concerns about what happens next at Credit Suisse and what that means for investors and employees.
The Swiss central bank said Sunday's deal includes 100 billion Swiss francs ($108 billion) in liquidity assistance for UBS and Credit Suisse.
Credit Suisse shares had lost a quarter of their value last week.
The bank was forced to tap $54 billion in central bank funding as it tries to recover from scandals that have undermined confidence.