* German inflation undershoots, confirming Draghi warning
* Italian bonds knocked by election fears but debt sale flies
* Greece denies report it may opt out of bailout money (Adds German CPI, updates prices)
LONDON, May 30 (Reuters) - German government bond yields fell to their lowest level in more than a month on Tuesday as inflation slowed in the bloc's biggest economy, underscoring the challenges the European Central Bank faces in normalising monetary policy.
German consumer inflation eased more than expected in May to fall below the European Central Bank's price stability target of just under 2 percent.
This further tempers expectations for policy tweaks at the central bank's June 8 meeting following cautious comments from ECB chief Mario Draghi on Monday.
While some policymakers are calling for an end to aggressive bond purchases and sub-zero rates as growth recovers, Draghi told the European Parliament that inflation remained subdued and the bloc still required substantial stimulus.
Spanish inflation rose 2 percent year-on-year in May, in line with a Reuters forecast but down from a previous reading of 2.6 percent.
"Our expectations are that the peak of inflation in the euro zone - and therefore the height of pressure on the ECB to tighten policy - is now behind us," Mizuho strategist Antoine Bouvet said.
"There will always be a debate between the dovish and hawkish camps at the ECB, but this gives the dovish camp more of an edge ahead of the June 8 meeting."
The bloc's benchmark German 10-year yield fell to 0.29 percent in early trading, its lowest since April 25, and was steady at around 0.30 percent thereafter.
A key market gauge of long-term euro zone inflation, the five-year five-year forward rate, was at its lowest since early April.
But it was not only doubts about inflation that kept up demand for the safe-haven debt, as the possibility of early elections in Italy knocked lower-rated bonds in southern Europe.
Italian 10-year yields climbed as much as 4 basis points to a near two-week high of 2.21 percent, dragging up yields in Spain by a similar amount.
The spread between Italian and German 10-year borrowing costs hit its highest level in nearly four weeks at 191 basis points.
Prime Minister Matteo Renzi said on Sunday that it made sense "from a European perspective" for Italy's next election to be held at the same time as Germany's, scheduled for September.
Investors have been worried about the rise of the anti-euro 5-Star Movement, which has led some polls recently, and what it might mean for Italy's future in the single currency bloc. Polls point towards a hung parliament.
Despite this, Italy sold 7.5 billion euros of 5- and 10-year bonds at their lowest yields in five months at auction on Tuesday.
Elsewhere, Greece denied a German newspaper report it could opt out of receiving bailout loans needed to make a July debt repayment if its lenders failed to offer clear debt relief terms to the country despite it having passed more reforms.
Greece's finance minister said on Monday that creditors needed to reach a deal on debt relief measures at the next meeting of euro zone finance ministers in June.
Greek 10-year government bond yields edged higher by 3 bps to 6.03 percent, while the short-dated two-year bond yields were up 5 bps to 5.83 percent.
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(Editing by Jeremy Gaunt)