* Economy head - EU has plan if stress tests find problem
* Rehn - countries can use 500 billion euro safety net
* Message designed to win back investor confidence
(Recasts, updates with Rehn comments, adds background)
By John O'Donnell and Marcin Grajewski
BRUSSELS, July 5 (Reuters) - European Union countries that discover problem banks when they stress-test their lenders could turn to an existing EU state back-up scheme, the bloc's economy chief said on Monday.
EU Economy Commissioner Olli Rehn said that should any government exhaust national funds in helping a troubled lender, it could turn to "EU financial backstops ... in the second line of defence."
"In order to use these European financial stability mechanisms in the case of any country we would need to have a programme ... focused in particular on the restructing of the banking sector and addressing the potential needs of a possible recapitalisation," Rehn told lawmakers in the European parliament. "That is the strategy."
It is the first time the European Commission or executive has spelt out that countries struggling to recapitalise stricken banks could tap a 500 billion euros scheme set up as a safety net should borrowing problems in Greece spread to Spain and beyond.
By explaining what it would do should "pockets of vulnerability" be uncovered by stress testing, Rehn hopes to win back the confidence of jittery investors.
Many are nervous that wider stress-testing of European lenders could exacerbate problems of a cash-strapped state which is suddenly forced to shore up the finances of one of its banks which fails to come up to scratch. Rehn also partially described one of the test criteria, which has proven controverial.
"We are including the criteria of sovereign debt shock in order to reinforce the credibility of results," he said, without shedding further light on how this would be tested.
Some countries are nervous that placing too high a hurdle for banks in this regard, for example by simulating a default by countries like Greece, could shatter investor confidence.
Rehn said that the testing of banks would now be wider than originally planned. The 27-country bloc had set out to examine just 25 of its biggest banks.
"We are testing more banks including second-tier banks. For instance, regional banks," he said. "This gives a clear and more accurate picture of the resiliance of the whole European banking sector."
The European Commission or executive helps set the criteria for testing alongside the bloc's countries and the European Central Bank. (Editing by David Gregorio)