UPDATE 1-EU economy rebounds but shadow over banks

* EU paper: bank stress tests should be done annually

* Bank profits expected to come under long term pressure

* Making national bank levies compatible a "difficult" task

(Adds more quotes, background, bank levy paper)

By Huw Jones and John O'Donnell

BRUSSELS, Sept 29 (Reuters) - European Union recovery broadened in the second quarter and inflation is moderate but banks should face annual health checks as they face many risks, a paper for the bloc's finance ministers said. Exports sparked the rebound but there are concerns over emerging and sovereign debt markets according to the "key risks" paper which examines the economy since April this year.

It will be discussed by EU finance ministers on Thursday and Friday.

The recovery conceals high divergences across member states but "inflation rates in the EU are set to remain moderate," the paper obtained by Reuters said.

Also "some concerns are related to the risk of overheating in emerging markets".

Bank earnings have bounced back but this may not last as they face debt funding pressures and risks from their exposures to large companies and corporate property markets.

"In the longer-term the sustainability of banks' earnings is not ensured as the previous increase in profits was mainly caused by the reduced impairment on loans and banks' provisioning," it said.

Governments in Britain, Germany, Belgium and elsewhere were forced to use billions of euros of taxpayer money to shore up a banking sector that went into near meltdown after the collapse of U.S. Lehman Brothers bank two years ago.

The European Central Bank has been gradually phasing out the emergency support it has given to banks since the financial crisis intensified in 2008, although it has been forced to slow that process by the ongoing euro zone debt crisis.

The "present outlook suggests that, for many banks, the conditions for exit from the support measures are not favourable and exits should be carefully assessed."

ANNUAL HEALTH CHECK

The paper also said that this summer's stress tests of banks organised by the Committee of European Banking Supervisors (CEBS) had helped to stabilise sentiment.

"The CEBS's stress test has proved to be an important supervisory tool to assess the resilience of banks and should become an ordinary practice in the EU, to be repeated on a yearly basis."

Sovereign debt markets, highlighted by the plight of Ireland, Greece and Portugal, remain fragile.

"It is of concern that one quarter of the bonds to be refinanced over the next six months is attributed to banks in member states subject to higher market perception of sovereign risk," the paper added.

With sovereign risk showing a close interdependence with the fragilities affecting the banking sector, concerns have now shifted from banks' solvency to their refinancing ability.

COMMON BANK LEVY DIFFICULT

European finance ministers will also make a renewed attempt to find a single approach to taxing banks more to pay for any bailouts when they gather on Thursday and Friday.

But they appear increasingly resigned to being unable to settle their differences on the matter, according to a separate document prepared by officials ahead of their meeting.

Most European finance ministers agree that banks should pay more in the wake of an economic crisis that many blame them for causing but how to do this in practice remains tricky.

Sweden has already introduced a levy, while Germany and Britain have unveiled plans.

"Rendering these different national systems of levies fully compatible ... may prove to be a difficult task," officials write, adding that any new national levies should remain flexible so as to broadly fit within a European framework.