Euro zone government bond yields rose and spreads widened on Tuesday after inflation data cemented investors' concerns that the European Central Bank might accelerate its monetary tightening path.

Inflation rose to another record high in May, beating analysts' forecasts and indicating that it is no longer just energy pulling up the headline figure.

Money markets increased their bets on future European Central Bank rate hikes, discounting 115 basis points (bps) by year-end from 110 bps last week. They are also pricing in a 35% chance of an additional 25 bps move beyond the 25 bps already fully priced in for July.

"Despite Lagarde's call for 'gradualism', which implies a 25 bps rate hike in July and an additional 25 bps move in September, the market continues to price the risk of 50 bps in July," said Rohan Khanna, research strategist at UBS.

ECB President Christine Lagarde has advocated a gradual approach to monetary tightening while asserting the ECB is free to react to the effects on the economy and the inflation outlook as rates rise.

Germany's 10-year government bond yield, the bloc's benchmark, rose 4 bps to 1.087% after hitting an almost two-week high at 1.093%.

The two-year yield, more sensitive to the ECB rate hike path, was up 3.5 bps at 0.472%, its highest since November 2011.

"The market is discounting an 8.8% peak for the HICP (harmonised index of consumer prices) in September, so the inflation story in Europe is not over," UBS' Khanna argued.

"In this scenario, it's fair for the market to price a risk premium for a faster pace of normalisation, which involves a bearish picture for the fixed income market," he added.

Italy's 10-year government bond yield rose 10 bps to 3.092%, its highest since May 10.

The spread between Italian and German 10-year bond yields rose 8 bps to 200 bps.

Expectations of a more aggressive tightening path widen spreads between core and peripheral bond yields as more indebted countries benefit the most from low interest rates.

A key market gauge of long-term euro zone inflation expectations rose to a one-week high at 2.1626% from 2.1271% late on Monday.

Deutsche Bank expects "a long period of high inflation where second-round effect and wage pressures can build."

Unicredit analysts argued the situation in longer-term "expectations might remain vulnerable until the peak in realised inflation is over, which we think will be the case with the release of July" data.

(Reporting by Stefano Rebaudo, Editing by Catherine Evans)