* Euro zone yields a touch lower
* Markets steady after last week's beating
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices, adds quote )
LONDON, July 3 (Reuters) - Germany's 10-year government bond yield pulled back from 3-1/2 month highs on Monday, as markets showed signs of stabilising from heavy selling last week prompted by jitters that ECB monetary stimulus could be unwound in the months ahead.
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.
But in a sign that the heavy selling seen across world bond markets last week was abating for now, bond yields in the euro zone fell 2-4 basis points. When a bond's price rises, its yield falls.
In Germany, the bloc's benchmark issuer, Bund yields edged back from 3-1/2 month highs touched at 0.498 percent and were down 2 bps 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 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.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s
(Reporting by Dhara Ranasinghe; Editing by John Stonestreet and Andrew Heavens)