* German inflation remains well below target
* Bond yields head back towards lows
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates with nationwide German inflation number)
LONDON, June 27 (Reuters) - Germany's government bond yields fell back towards record lows on Thursday after data showed annual inflation in the euro zone's biggest economy remained well below the European Central Bank's target in June.
Bond yields had inched higher earlier in the session as hopes for a U.S.-China trade deal and state inflation numbers from Germany put some upward pressure on borrowing costs.
In North Rhine-Westphalia, Germany's most populous state, inflation accelerated to 1.7% from 1.6%. In Bavaria, consumer prices rose by 1.8% after a 1.6% increase in May.
But the nationwide number showed German consumer prices, harmonised to make them comparable with inflation data from other European Union countries, rose by 1.3% year-on-year in June after increasing by the same amount in the previous month.
"At the start of the day we had optimism about trade and during the day the German inflation number came out that was only in line with expectations, so that was the main driver for lower yields," said DZ Bank rates strategist Sebastian Fellechner.
In late trade, Germany's 10-year bond yield was down 1.2 basis points at minus 0.32%, nearing Tuesday's record low of minus 0.336%.
Most other 10-year yields in the bloc were about one bps lower on the day, reversing earlier rises of around 2 bps.
The overall inflation data from Germany only reinforced expectations for further monetary easing from the European Central Bank, analysts said.
"As so often over the last years, if inflation is not even picking up in Germany, with a strong labour market and an economic expansion of 10 years, where else in the eurozone should it pick up?," ING chief economist Carsten Brzeski said in a note.
European Commission data meanwhile showed euro zone economic sentiment dropped to its lowest point in nearly three years in June with confidence falling markedly in Germany and Italy.
That backdrop has been favourable for euro zone issuers to come to the markets.
Austria this week was able to place a five year bond at a yield of -0.435%, becoming the first euro zone sovereign to price a public sale of debt below the -0.40% deposit rate.
It also reopened its 100-year bond to raise an additional 1.25 billion euros
Italy followed up on Thursday by selling five and 10-year bonds at their lowest yields in more than a year. (Reporting by Virginia Furness and Dhara Ranasinghe)