Sept 12 (Reuters) - Euro zone government bond yields steadied on Tuesday while money markets slowly increased their bets on an additional rate hike by the European Central Bank.

Investors are almost evenly split about this week's decision as ECB euro short-term rate (ESTR) forwards price in a 45% chance of 25 basis points (bps) from around 40% the day before.

They are more certain about an ECB move by year-end pricing an around 80% chance, with no further tightening afterwards. It was at 75% on Monday.

German wholesale prices fell for the fifth month in August due to lower prices for mineral oil products, data from the federal statistics office showed on Tuesday.

Germany's 10-year government bond yield, the benchmark for the euro area, was flat at 2.36%.

Oil prices recently triggered concerns about the inflation outlook.

The Brent crude futures held above $90 a barrel on Tuesday after reaching that level for the first time in 10 months last week as Saudi Arabia and Russia announced they would extend voluntary supply cuts.

Analysts argued that investors were positioning for Thursday's ECB policy meeting and crucial inflation data in the U.S. on Wednesday.

"A hawkish tone from the U.S. CPI data and a hike from the ECB could give front-end rates a larger lift this week and provide the ingredients for a brief curve-flattening episode," said Benjamin Schroeder, senior rate strategist at ING, in a research note.

U.S. inflation figures could add to a growing view that the Federal Reserve will keep interest rates steady when policymakers meet next week.

Recent comments from Fed officials have indicated the Federal Reserve is content to keep rates steady at its next policy meeting on Sept. 19-20 but is not ready to declare the war on inflation is over.

Italy's 10-year government bond yield, the benchmark for the euro area periphery, was unchanged at 4.39%.

The spread between Italian and German 10-year yields -- a gauge of investor sentiment towards the euro zone's more indebted countries – was at 175 bps, just off its widest level in two months.

Some market participants expect an acceleration of quantitative tightening measures – which involve the ECB reducing its bond portfolio – might hurt peripheral bond prices.

Bond yields move inversely with prices.

ECB hawks have called for ending reinvestments from bonds bought under the 1.7 trillion euro ($1.82 trillion) Pandemic Emergency Purchase Programme (PEPP) earlier than the current end-2024 deadline.

Elsewhere, Britain's labour market showed more signs of cooling in the three months to July despite another month of strong pay growth marginally affecting gilt prices.

(Reporting by Stefano Rebaudo, editing by Ed Osmond)