* Euro zone yields a touch lower
* Markets steady after last week's beating
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Rewrites top, updates prices)
By Dhara Ranasinghe
LONDON, July 3 (Reuters) - Germany's 10-year government bond yield edged higher to hit a fresh 3-1/2 month high on Monday, with the market still plagued by jitters that ECB monetary stimulus could be unwound in the months ahead.
The yield on the region's benchmark bond came within a whisker of 0.50 percent, a level that -- with the exception of one session in mid-March -- was last seen in January 2016.
Remarks last week from European Central Bank President Mario Draghi that the central bank could make tweaks to its policy to accompany the recent economic recovery triggered the biggest weekly jump in Bund yields since December 2015.
The ECB is working on moving away from its ultra-easy monetary policy, Jens Weidmann, head of Germany's Bundesbank and an ECB policymaker, said on Saturday.
Data on Monday provided fresh signs that the euro zone economy is gaining momentum. Factories in the bloc rounded off the first half of 2017 by ramping up activity at the fastest rate for more than six years, a survey showed.
Though the market was generally far more stable on Monday, higher-rated bond yields were flat to a basis point higher on the day.
In Germany, the bloc's benchmark issuer, Bund yields touched 0.498 percent before settling at 0.48 percent near the close, up a basis point on the day.
"The market reaction last week was very sharp and now is probably the time to digest recent comments," said Patrick Jacq, European rates strategist at BNP Paribas. "July could be a more supportive month for bonds as there is less supply, but clearly the trend is now upwards for yields."
Bund yields have almost doubled within the space of a week. They could break above 2017 highs at around 0.51 percent soon as investors position for tighter monetary policies globally, analysts said.
U.S. Treasury yields rose to six-week highs on Friday as inflation data was not considered weak enough to delay Federal Reserve plans to hike interest rates.
Bank of England Governor Mark Carney said last week that Britain's central bank was likely to debate a rate increase in coming months, fuelling a sell-off in global debt markets.
Comments from Bank of Canada policymakers last week have ramped up market expectations for a rate hike in July and the Reserve Bank of Australia meets on Tuesday, with the focus on whether it will also talk about the need for tighter monetary policy.
"Whether we can stabilise this week will depend on the U.S. jobs report," said Peter Chatwell, head of euro rates strategy at Mizuho, referring to U.S. non-farm payrolls data due on Friday.
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Reporting by Dhara Ranasinghe; Editing by John Stonestreet and Andrew Heavens