European Central Bank officials say there is "no room for complacency" even though stresses from the debt crisis have eased on banks and financial markets.
The central bank for the 333 million people in the 17-country eurozone on Friday warned that failure by governments to reduce deficits and improve growth risked worsening the situation again.
And European leaders need to press on with building new rules and institutions to safeguard the euro, the bank added in its twice-yearly financial stability report.
"Key financial stability risks remain and there is no room for complacency," the bank said.
Europe is struggling with high levels of government debt in some countries, financially weak banks, and sluggish economic growth. Greece, Ireland and Portugal have needed government rescue loans, although Spain and Italy are now breathing easier after struggling to finance themselves over the summer.
The bank noted "a tangible easing of euro area financial stability strains since the summer."
Bond markets have improved dramatically since ECB President Mario Draghi vowed in July to do "whatever it takes" to save the euro. The ECB then outlined a plan under which it would buy unlimited amounts of a country's government bonds, reducing its borrowing rates, on condition it tapped a European aid program.
But ECB Vice President Vitor Constancio was cautious when asked Friday at a news briefing about the eurozone's progress out of its financial and economic troubles.
"I have learned with ancient Greece, not to be hubristic," he said, using the Greek word for excessive pride and self-confidence. "There is an improvement."
The ECB report said there was a risk that the improvement in market conditions might reduce the pressure on governments to cut debt and deficits and improve growth.
Banks also remain a potential weak spot as they repair their finances, Constancio said. The banking system also remains fragmented, with borrowing costs far higher in some countries than in others, even though they share a common benchmarket interest rate set by the ECB.
On the bright side, banks in financially troubled countries are able to tap bond markets again. Meanwhile borrowing costs have fallen for governments.
On Thursday, EU finance minister struck a deal that would create a single central bank supervisor under the aegis of the ECB. The idea is to have a watchdog that will not put off taking action when banks are getting into trouble, as overly protective national regulators have done during the crisis. That, in turn, means governments will be less likely to face huge costs from having to the banks out.
European leaders and many analysts say the single supervisor agreement is progress. However, the leaders have put off to next year — or beyond — decisions on other key changes to strengthen the euro.
One of the next steps they will consider next year is the creation of a central authority that can restructure banks and force losses on bond holders. Prospects are uncertain for other, more controversial proposals, such as a central fiscal authority that would try to even out economic downturns across eurozone countries, common borrowing, and EU-wide bank deposit insurance.