* ECB's Coeure sees rates staying at "very low levels"
* Up to 30 bln euros of bond supply due this week
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices, adds quote, chart)
LONDON, March 12 (Reuters) - Most government bond yields in the euro area fell on Monday after ECB executive board member Benoit Coeure said short-term interest rates would stay at "very low levels", supporting a view that any exit from hefty stimulus will be slow.
A busy week for euro zone bond supply exerted some upward pressure on borrowing costs. But Coeure's comments early on Monday underpinned sentiment coming just days after the ECB gave up a pledge to increase bond purchases if needed and signalled a slow route out of its stimulus.
Coeure added that inflation was not quite where the European Central Bank "would like it be".
Germany's benchmark 10-year bond yield dipped 1 basis point to 0.64, heading back towards last week's five-week lows . German short-dated bond yields also fell, while yields on other higher-rated bonds were down 1-2 bps. .
"Two-year rates are a bit lower so that ties in with dovish comments from Coeure, but what he said is in line with (ECB President Mario) Draghi's dovish comments last week," said ING senior rates strategist Martin van Vliet.
According to a source-based story on Friday, ECB staff offered policymakers meeting last week a scenario where interest rates would be raised in mid-2019 after winding down their bond purchases at the end of this year.
A perception that a rise in ECB interest rates remains some way off contrasts with expectations for another U.S. rate rise later this month, confirmed by Friday's strong jobs data and keeping the gap between U.S. and German bond yields wide.
The U.S./German 2-year yield spread was at 282 basis points, , close to its widest in over 20 years. The gap between 10-year U.S. and German bond yields was at 226 bps and hovering close to its widest in around 14 months .
"The lack of reaction to the strong U.S. jobs report in European fixed income is a sign that the ECB meeting last week, by showing no inclination to rush toward the exit, has given fresh legs to the U.S.-Europe divergence trade," said Mizuho rates strategist Antoine Bouvet.
Anticipation of heavy bond supply this week limited the fall in bond yields. The Netherlands, Italy, Germany, Portugal, France and Spain are expected to auction up to 30 billion euros of bonds between them.
Analysts said uncertainty over the make-up of the next Italian government after an inconclusive March 4 election was starting to weigh on Italian bonds.
The Italian/German 10-year yield gap was at 138 bps versus 135 bps on Friday.
"It is an open race as to who will form the next Italian government and this uncertainty is starting to weigh on spreads," said DZ Bank rates strategist Daniel Lenz.
(Reporting by Dhara Ranasinghe editing by Mark Heinrich)