The European Central Bank said today that record low interest rates were putting insurance firms and banks under increasing pressure.
In its twice-yearly Financial Stability Review, it also warned that any sell-off in stocks and bonds could damage the euro zone's recovery.
The ECB also said risks from Greece for the euro zone's governments had "increased sharply" but that their borrowing costs and growth prospects were being helped by measures like the ECB's bond-buying programme.
The negative side-effect of that, though, was the squeeze it was putting on insurance firms who are finding it increasingly difficult to find assets that pay out enough to cover their costs.
It was also putting pressure on banks in terms of their profitability.
The ECB's message echoes similar warnings from the International Monetary Fund and one of Europe's top regulators earlier this month.
"Such market conditions pose a significant challenge for some insurance companies' profitability in the medium term, with the potential to erode capital positions in the long run," the ECB report said.
"The impact of the low interest rate environment is particularly relevant for those life insurers that have locked in high return guarantees and have large asset/liability duration gaps."
Overall the ECB said there were four main risks to euro zone financial stability at present.
The bank's Vice President, Vitor Constancio, said the biggest was that a sharp bond and stock market sell-off could derail the bloc's still fragile economic recovery.
He also flagged worries such as debt sustainability concerns in the sovereign and corporate sectors, bad loans still plaguing banks' books and the growth of lesser-controlled 'shadow' parts of the banking system.
"Benign financial market conditions may obscure the urgency of fiscal and structural reforms. If key reforms were to be delayed, a reassessment of sentiment towards euro area sovereigns is possible," the report added.
The recent decline in market liquidity was also raised.
Constancio said it was of biggest concern in the bond market, where the ECB has been hoovering up much supply for its quantitative easing programme.
On Greece, he said he was confident it would not leave the euro. It could default on its bailout loans, however.
"The end result is that a Greek exit will not happen," Constancio said, adding: "That's not to exclude several things that are not nice that may happen."
Commenting on the state of Greece's banks in the event of default, he said: "They can sustain the impact of a big potential impairment in Greek public debt."
He also hinted the ECB would not automatically cut them off from its emergency funding.