* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr
LONDON, Jan 7 (Reuters) - Euro zone government bond yields edged up from around three-week lows on Tuesday as fears of an all-out conflict between the United States and Iran abated, reducing demand for safe-haven assets.
Oil prices also gave up some of their gains as investors reassessed Middle East risks after a U.S. air strike killed a top Iranian commander on Friday.
"The knee-jerk reaction to the air strike, with equities sliding and bonds rallying, has petered out as so far there is no follow through although the situation remains dire," said Christoph Rieger, rates strategist at Commerzbank.
Most 10-year euro zone bond yields were higher in early trade. Germany's Bund yield was up 1 basis point at -0.28% -- rising from more than three-week lows on Monday at -0.31% but below last week's seven-month highs.
Focus turned to the euro zone "flash" inflation estimate, due this session. Economists polled by Reuters forecast headline euro zone inflation rose 1.3% year-on-year in December, up from 1% previously. Excluding volatile food and energy prices, inflation is forecast at 1.5% versus 1.4% a month earlier.
If U.S.-Iran tensions lead to a prolonged rise in oil prices, inflation expectations and bond yields in the euro zone will rise with them.
A key gauge of inflation expectations, the five-year, five-year breakeven inflation forward, has been little moved by oil markets in the past year as concern over economic growth dragged it lower.
The market gauge, tracked by the European Central Bank, has risen from last year's record lows. But at around 1.3%, it remains below the ECB's inflation target of just under 2% .
Jim McCormick, global head of desk strategy at NatWest Markets in London, says markets are under-pricing potential inflation risks.
"Our core inflation surprise index has risen since the middle of 2018 and judging from Friday's France and German data, euro area core inflation may surprise to the upside for a third month in a row," he said in a note.
Data released on Friday showed German annual inflation rose by 1.5% year-on-year in December after increasing 1.2% in November. French inflation rose 1.6% year-on-year in December, beating analyst expectations.
(Reporting by Dhara Ranasinghe, editing by Larry King)