* Gilts pull down major govt bond yields in Europe and U.S.
* Germany's yield falls after touching three-week high
* Upbeat German data, U.S. payrolls weigh on bond sentiment
* Upcoming euro zone debt supply in focus (Writes through)
By Dhara Ranasinghe and Abhinav Ramnarayan
LONDON, Jan 9 (Reuters) - Euro zone government bond yields fell on Monday after comments by British Prime Minister Theresa May fuelled expectations of a "hard Brexit" and increased demand for safe haven assets.
German bond yields, the region's benchmark, fell from earlier highs as UK Gilts dragged major low-risk government bond yields lower.
Sterling was on track for its biggest losses in three months while the yield on 10-year Gilts fell by 4 basis points (bps) to 1.34 percent after May said she was not interested in keeping "bits" of Britain's EU membership.
"Safe haven markets tend to correlate and I do think that is what is driving U.S. and European yields lower this afternoon," said Rabobank strategist Richard McGuire.
Germany's 10-year bond yield fell 2 bps to 0.28 percent, after hitting a high of 0.32 percent earlier in the session.
The fall in yields is a reversal of the prevailing sentiment in bond markets so far this year, with yields rising on the back of increased expectations of global growth and inflation.
Data on Monday showed German industrial production rose for the second consecutive month in November and exports jumped more than expected, boosting expectations for a rebound in Europe's biggest economy in the fourth quarter.
Together with Friday's U.S. jobs numbers showing a rebound in wages last month, this adds to growing signs of a pick-up in inflation and economic growth that suggests the tide has turned for a three-decade bull run in bonds.
A number of hawkish comments from U.S. Federal Reserve officials also weighed on sentiment. Chicago Federal Reserve President Charles Evans added following the jobs numbers that the central bank could lift interest rates three times this year, faster than he expected just a few months ago.
Most other euro zone bond yields also gave up early rises and were lower, with southern European bond yields down 5-7 bps.
Analysts said that was probably a correction from a sharp sell-off last week. They expected yields to come under pressure from a slate of heavy bond supply this week, while sentiment towards Italian bonds could be put to the test ahead of a key DBRS ratings review on Friday.
The Netherlands, Austria, Germany and Italy hold auctions this week, while Portugal is expected to sell a 7-or 10-year bond via a group of banks. Analysts at Mizuho also expect Belgium to sell a 10-year bond via a syndicate of banks this week. (Editing by Mark Potter and Alexander Smith)