* Key risk event week for markets; ECB meets Thursday
* ECB expected to take more benign view of economy
* German Bund yields hover near 1-month lows
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr
LONDON, June 5 (Reuters) - German benchmark government bond yields hovered near one-month lows on Monday, with bond investors confident that the European Central Bank will this week only take baby steps towards unwinding its extraordinary stimulus.
The ECB, which meets on Thursday, is set to take a more benign view of the economy and will even discuss dropping some of its pledges to ramp up stimulus if needed, sources with direct knowledge of the discussions told Reuters last week.
An improving economy and some fading of euro zone political risks following French presidential elections in April and May have boosted speculation about a scaling back or "tapering" of the ECB's massive asset-purchase scheme in coming months.
But with the ECB expected to strike a cautious tone because of doubts around inflation, bond investors seem largely unruffled.
Data last week showed inflation in the euro area slowed to 1.4 percent year-on-year in May, from 1.9 percent in April. The ECB targets inflation of just below 2 percent.
"The data, especially the inflation numbers, have not been strong enough to suggest a hawkish tone from the ECB this week," said Orlando Green, European fixed income strategist at Credit Agricole. "They are likely to leave things as balanced as possible."
Germany's benchmark 10-year bond or Bund yield was trading just 1.5 basis points higher on Monday at 0.29 percent and within sight of one-month lows hit last week, while short-dated bond yields remain deep in negative territory .
Money market pricing also suggests investors are not anticipating a rate hike within the next year.
"The (ECB Governing)Council sounds confident enough to upgrade the balance of risks to growth, but the conviction in inflation is not there yet," Deutsche Bank analysts said in a note.
Weaker-than-expected U.S. employment data on Friday has also cemented a view that while the U.S. Federal Reserve is likely to raise rates when it meets next week it is likely to be cautious about further rate increases.
In the U.S., long-dated Treasury yields fell to nearly seven-month lows, and short-dated yields touched their lowest in more than two weeks after Friday's jobs report.
Analysts said safe-haven bond markets could draw support from uncertainty surrounding Thursday's general election in Britain, where seven people were killed in a militant attack in London at the weekend.
Polls show the election is much tighter than previously predicted. A close election could throw Britain into political deadlock just days before formal Brexit talks with the European Union are due to begin on June 19.
Across the euro zone, 10-year bond yields outside Germany were 1-2 basis points higher on the day with trading subdued by a public holiday in a large swathe of the bloc.
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(Reporting by Dhara Ranasinghe; Editing by Raissa Kasolowsky)