* Coeure calls for ECB to police all banks
* Bundesbank President sets down conditions for support
* Contrasting message underscores divisions over banking union
By John O'Donnell and Eva Kuehnen
BRUSSELS/FRANKFURT, Nov 19 (Reuters) - The European Central Bank on Monday said that it should have the power to supervise all lenders in a banking union, a demand the president of Germany's influential Bundesbank was quick to temper.
After three years of piecemeal crisis-fighting, European countries are attempting to agree on a banking union to lay a cornerstone of wider economic integration and protect the euro.
It marks the first attempt to unify the bloc's response to problem lenders.
But the reform has divided Europe, fuelling tensions that were once again evident in the contrasting messages given by the French member of the ECB's Executive Board and the president of the Bundesbank.
Speaking in Brussels, ECB executive board member Benoit Coeure said: "It is crucial that all banks are covered by the SSM (single supervisory mechanism)."
Such as move would mean the ECB would supervise a broad range of lenders, from large European multinationals to small local banks.
The remarks from a member of the body that forms the nucleus of the broader Governing Council puts the ECB at odds with the German government, which wants to keep primary oversight of the community savings banks in the country, and is seeking to limit the ECB's remit to systemically important lenders.
But Coeure warned that failing to give the ECB broad scope would undermine banks that do not come under its supervisory watch. His fear is that banks outside the scheme would be viewed as less secure, making it harder to keep deposits or funding.
"A two-tier system would result in an uneven playing field, effectively segmenting the banking sector, which is precisely what we are trying to repair," he said.
Making the ECB the supervisor for lenders chiefly in the 17 countries that use the euro would be the first of three pillars in a banking union and one EU leaders have committed to complete by the year-end.
But Jens Weidmann, the Bundesbank president, warned that the new scheme of supervision should not "overshoot the mark" and emphasised the need for national supervisors to keep responsibility where risks were shouldered by individual countries and advocated rules on winding down banks in crisis.
"National responsibility can remain, where risks can be borne at the national level and there is no danger for the taxpayers of other member states," he said.
He also argued for a strong system to tackle troubled banks. "Where risks are covered at the European level, there must also be the possibility for joint control and intervention," he said.
Weidmann also demanded a clear separation of the tasks of monetary policy and supervision at the ECB and a stronger German voice when voting on banking supervisory matters.
"There is a conflict of interest between banking supervision and monetary policy in the practical implementation," Weidmann said.
His remarks will fuel growing concern in Brussels that the banking union construct risks crumbling.
The German government wants the ECB's supervision limited because it is worried that the more banks are included in the scheme, the higher the potential cost when, as is ultimately planned, supervision is backed up by a central fund to pay for the closure of troubled lenders.
Weidmann warned that if the banking union were to lead to joint liability for individual state debts and allow countries to run up borrowings, then it would undermine the currency. "This risk exists, and I think we should not underestimate it."
When supervision is in place, it would pave the way for the euro zone's rescue fund, the European Stability Mechanism, to help troubled lenders directly rather than via their governments.
Complementing the new supervisory regime with two additional pillars - a central scheme to wind down banks and a combined means of deposit protection to prevent bank runs - would complete the banking union.
Weidmann pointed out that the third aspect of establishing a joint deposit guarantee scheme - which Germany opposes - had moved to the background, "in my view rightly so".