EU banks have borrowed less than expected from the European Central Bank, easing concerns about liquidity among financial institutions.
After Tuesday's sharp falls, stock markets and the euro stabilised on news that the ECB had agreed three-month loans worth 131.9bn euros (£108bn).
This compared with the 150bn to 200bn euros many had expected.
The euro rose almost a cent against the pound, while European stock markets also made small gains.
"It certainly implies that strains in the wholesale funding market are less acute than some feared, and that fewer banks than it was thought are being deprived of finance from commercial sources," said BBC business editor Robert Peston.
But he added that, given that it was more expensive to borrow from the ECB than from other banks, it would be "foolish to argue that eurozone banks are in tip-top condition".
Banking shares had been under pressure after the European Central Bank confirmed it would be stopping a special 12-month loan facility for euro-zone lenders from Thursday.
Investors were concerned that European banks could face funding problems as a result.
'Rigorous and credible'
Also this week, the EU has said it is to treble the number of banks that will be subject to public stress tests, as it tries to allay a growing global anxiety over Europe's finance sector.
The tests are designed to examine how certain banks would perform if there were a repeat of the financial crisis.
The plight of Greece, combined with worries about nations such as Spain and Portugal, means that for the first time the tests would also examine whether institutions could cope in the event of a sovereign-debt default in the eurozone.
The number of those forced to take part in the exercise would expand from the 22 big banks examined last year to include a further 60 to 120 banks, meaning that many not included in last year's stress-tests will now feature.
They include, for the first time, banks such as German Landesbanken, which are not among the biggest institutions but whose potential weaknesses have contributed to uncertainty in financial markets.
The tests are due to be completed by mid-July, with results to be issued on a bank-by-bank basis.
A spokeswoman for EU internal markets commissioner Michel Barnier said the tests were tougher and more transparent, adding they were also "more rigorous and credible".