* Nagel warns against trying to set spreads
* Sets conditions for his approval of any aid
* Bundesbank chief objected to decision on June 15
* Bundesbank is ECB's largest shareholder (Recasts with comments from Nagel, de Guindos)
By Balazs Koranyi and Francesco Canepa
FRANKFURT, July 4 (Reuters) - The European Central Bank's biggest shareholder, Germany's Bundesbank, laid out its conditions for providing fresh support to the euro zone's most indebted countries on Monday after opposing such aid at an emergency meeting last month.
ECB policymakers pledged to buy more bonds from debt-laden countries such as Italy at an emergency meeting on June 15 to contain a widening spread between their borrowing costs and Germany's as the central bank prepares to raise interest rates.
But Nagel, who disagreed with that decision according to sources at the meeting, warned on Monday against trying to decide the right market spread as that was "virtually impossible" and risked making governments complacent.
"I would thus caution against using monetary policy instruments to limit risk premia, as it is virtually impossible to establish for sure whether or not a widened spread is fundamentally justified," Nagel said in a speech.
Speaking soon after Nagel, ECB vice-president Luis de Guindos said it was critical to prevent financial fragmentation between the euro zone's 19 countries if the ECB was to raise interest rates and fight high inflation - a hot topic in Germany.
It was the first visible disagreement between Nagel and Christine Lagarde's ECB since the former took office in January and tried to end years of conflict between both institutions.
The ECB is trying to bring down yield spreads by using proceeds from maturing bonds in Germany, and other north European nations, to buy more Italian, Greek, Spanish and Portuguese debt. It is also working on a new tool to buy even more southern European bonds with fresh money.
This will likely leave Germany falling below its quota of the ECB's bond holdings, as the purchases of peripheral bonds are unlikely to be matched by larger buying of core paper in the future, the sources said.
Nagel set out his conditions for backing a new spread-fighting scheme.
He said such help should only come in exceptional circumstances and with narrowly defined conditions - likely a reference to countries showing financial prudence.
It should not get in the way of the ECB's efforts to bring down inflation or lessen the pressure on governments to run sound budget policies, Nagel added.
"Unusual monetary policy measures against fragmentation can only be justified in exceptional situations and under narrow conditions," Nagel said.
Sources have told Reuters the new instrument to buy more southern European bonds is likely to come with strings attached, such as that a country's debt is deemed sustainable by the ECB or that it complies with the European Commission's fiscal rules and economic recommendations.
In another possible concession to Germany, the ECB would likely drain cash via "liquidity-absorbing" auctions, rather than outright bond sales that would cause selling central banks like the Bundesbank to record losses, the sources said.
ECB policymakers who have spoken since the June 15 meeting, including Belgium's Pierre Wunsch and the Netherlands' Klaas Knot, two key policy hawks, have backed Lagarde's pledge to fight fragmentation.
This meant that Nagel's opposition was unlikely to prove an insurmountable hurdle.
But it would be a setback for two institutions trying to get along after a decade of disagreements under Nagel's and Lagarde's respective predecessors - Jens Weidmann and Mario Draghi.
Lagarde has given national central bank chiefs a bigger say in policy meetings and Nagel had until now refrained from publicly criticising decisions.
But Nagel has come under pressure at home over the highest inflation-rate since the 1970s and the perception that ECB policy was designed to support indebted states such as Italy and Greece rather than keep prices in check. (Editing by William Maclean)