* Euro zone headline and core inflation up
* Euro zone bond yields pushed up by U.S. data
* Italian bonds recover, still weakest EZ debt market in Oct
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates with reaction to U.S. data)
LONDON, Oct 31 (Reuters) - Most euro zone bond yields edged higher on Wednesday after data pointed to further signs of strength in the U.S. jobs market, although nagging concerns about the economic outlook for the single currency bloc limited selling pressure.
U.S. private sector payrolls increased by the most in eight months in October, suggesting overall job growth accelerated this month. Other data showed U.S. labour costs accelerated in the third quarter.
Having shrugged off stronger-than-expected euro zone inflation data earlier in the day, euro zone debt yields headed higher as U.S. Treasury yields rose after the U.S. figures.
With the exception of Italy, most 10-year bond yields were last up 1-2 basis points on the day.
Euro zone inflation rose to 2.2 percent in October from 2.1 percent last month, holding above the European Central Bank's target of just below 2 percent for the fifth month running. Even underlying inflation picked up.
But the numbers failed to put a dent in fixed income markets - something analysts attributed to a focus on the uncertain economic outlook.
Data on Wednesday showed German retail sales fell 2.6 percent year-on-year in September. That followed Tuesday's weaker-than-expected euro zone economic growth numbers for the third quarter and weak GDP data for Italy.
"At the moment it looks like the market is paying more attention to the activity data such as Italian GDP and the retail sales data this morning," said Mizuho rates strategist Antoine Bouvet.
Those concerns about the euro zone growth outlook helped limit the rise in euro zone bond yields.
Germany's 10-year bond yield was up 1 basis point (bp) at 0.38 percent, off session highs of 0.40 percent. U.S. 10-year bond yields were around 3 bps higher on the day .
German Bund yields were set to end October down around 10 bps - reflecting concern about volatility in Italy, recent weakness in world stocks and growing worries about the economic growth outlook.
"If you would have told me at the start of 2018 that Bund yields would be where they are today, I would have said you are crazy," said Brian Giuliano, vice president, portfolio management for fixed income at Brandywine Global in Philadelphia. "One reason for this fall in yields is that growth has come off throughout 2018, another is the populist challenges in countries such as Italy."
In a note, HSBC fixed income strategist Wilson Chin said 10-year Bund yields could fall to 25 bps.
Italian bond yields were down 5-10 bps as a recovery in risk appetite spilled over into the Italian bond market.
Analysts said reports suggesting the Italian government may take longer to implement its plans to widen the country's budget deficit may have helped a recovery in Italian bonds, although the moves were relatively small given the scale of selling in recent months.
Italy remains the euro zone's weakest bond market with 10-year bond yields set to end October around 27 bps higher.
(Reporting by Dhara Ranasinghe; Editing by Angus MacSwan and Mark Potter)