Swiss private bankers say that clients have asked to withdraw large amounts of cash. The moves follow five years of negative interest rates. The policy, intended to keep the Swiss franc from appreciating, requires banks to pay to park money with the Swiss National Bank. Banks have passed a portion of the extra costs on to their most affluent customers.

The ECB will only start raising its key interest rate, currently set at minus 0.5%, once the eurozone inflation “robustly” meets the central bank’s target of just below 2%, Ms. Lagarde said. That is unlikely to happen for several years. The ECB has left open the option of cutting interest rates even further below zero if the economic outlook worsens.