"The people and the markets look to the ECB for solutions," Asmussen said, according to the text of a speech for delivery at a conference in Brussels.
"But there should be no illusion that the ECB can single-handedly ensure a plain sailing for our economies and the markets. There are limits of what we can do, and what we know."
ECB actions can have an immediate impact on markets, Asmussen said, adding that success with such short-term crisis fighting may also mean longer-term challenges are not addressed.
"Short-term fixes do not change the structural features of European economies and markets," he said. "Those depend on the countries' economic policies, which take time to design and implement. Firm commitments from governments can help reduce this uncertainty, but can never eliminate it."
The ECB cut interest rates to a record low on Thursday to breathe life into a deteriorating euro zone economy but steered clear of more dramatic measures such as buying government bonds or flooding banks with fresh liquidity.
"Our communication is walking a tightrope: markets need reassurance that the ECB will do what is within its power and mandate to guarantee that the euro will not to fail," Asmussen said. "At the same time, governments need to have the right incentives to tackle the longer-term challenges."
(Writing by Paul Carrel)
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