* ECB's Draghi says stronger euro may trigger more easing
* Low-rated euro zone yields also fall
* Greek yields edge up as market comeback frenzy fades (Updates prices into mid-day, adds fresh comments)
By Marius Zaharia
LONDON, April 14 Yields on government debt fell across the euro zone on Monday, with those on Bunds hitting 10-month lows after European Central Bank President Mario Draghi said a stronger euro might trigger further monetary easing.
In the clearest signal yet the ECB was prepared to launch a stimulative asset-purchase programme, Draghi said the exchange rate had become increasingly important to policy as inflation was closer to zero than to the bank's target of just below 2 percent.
Draghi's French colleague Benoit Coeure said the bank was ready to buy assets if deemed necessary. But he also said the fragmentation of the euro zone economy meant purchases of a single asset class, such as government bonds, could not be assumed to affect interest rates across all classes.
Italian 10-year bond yields fell 3 basis points to 3.19 percent, within touching distance of record lows. Spanish yields fell a similar amount to 3.16 percent.
"The market is still playing the bet that the ECB is going to do something," said Alan McQuaid, chief economist at Merrion Stockbrokers in Dublin.
German Bund yields, the benchmark for euro zone borrowing costs, were one basis point lower on the day at 1.50 percent, having dipped to a ten-month low of 1.491 percent earlier. The euro was a touch softer at $1.3856 but remained close to its strongest levels this year.
Despite Draghi sending a strong message to investors, the moves were relatively subdued, with analysts saying the market had sensed a lack of consensus among ECB policymakers over how to pursue any asset purchase programme.
"The overall message was that the ECB doesn't know what QE (quantitative easing) would look like, but they see it as a viable policy option," said Lyn Graham-Taylor, rate strategist at Rabobank.
Quantitative easing is jargon for central banks buying assets with newly printed money.
GREEK YIELDS RISE
Greece was the only market in which yields rose, as investors continued to book profits on the strongest bond rally in the euro zone this year. Ten-year yields added 8 basis points to 6.39 percent on Monday,
The profit-taking began just after Greece issued a new five-year bond on Thursday, coming back to the market just two years after restructuring its debt.
Some analysts said the bond's pricing at 4.95 percent was too aggressive, leaving no room for a further dip in yields in secondary markets. Others said that after one of the quickest post-default comebacks in recent history it was simply unlikely that the newsflow in Greece would improve even further.
Investors bid 20 billion euros for the 3 billion euro bond on Thursday, but all Greek bonds sold off on Friday. The new bond last yielded 5.14 percent.
"The initial impression was that the bond got good demand, but the distribution in the secondary market was weak," said Nick Stamenkovic, a strategist at RIA Capital Markets.
"They (Greece) still have structural problems ... and political issues. I wouldn't recommend chasing their rally. There's better value in Spain and Italy." (Reporting by Marius Zaharia; Editing by John Stonestreet)