June 23 (Reuters) - Euro zone government bond yields fell sharply on Friday after economic data fuelled concerns about the economy and expectations that the European Central Bank might not be able to go too far in raising rates.

France's dominant services sector unexpectedly shrank in June while business activity slowed notably in Germany.

Euro area business growth virtually stalled this month as the downturn in manufacturing deepened while activity in the bloc's dominant services industry barely expanded.

Germany's 2-year bond yield, the most sensitive to expectations for monetary policy, dropped 11 bps to 3.16%.

"Financial markets have had one of those switches in the narrative that happen occasionally and are starting to worry about higher interest rates driving recessions," said Paul Donovan, chief economist at UBS Global Wealth Management.

The German yield curve measuring the gap between 10-year and 2-year bond yields hit -81.5 bps, its deepest inversion since September 1992.

An inverted curve, which is usually a reliable indicator of a future recession, means markets are pricing events which would lead central banks to cut rates.

Germany's 10-year yield, the bloc's benchmark, fell 13.5 bps to 2.35%.

Money market bets on the ECB depo rate peak briefly rose above 4%, and German short-dated yields hit a fresh 3-month high early on Friday as central banks outside the euro area tightened their policy the day before.

The Bank of England raised rates by 50 bps and said there had been "significant" news suggesting British inflation would take longer to fall.

The Swiss National Bank and Norges Bank also tightened monetary policy, suggesting they could do more.

Late on Thursday, U.S. Chair Jerome Powell said the Federal Reserve would move interest rates at a "careful pace" from here.

December 2023 forwards on European Central Bank (ECB) euro short-term rate (ESTR) were at 3.88%, implying market expectations for an ECB depo rate at 3.98% by year-end.

Italy's 10-year government bond yield, the benchmark of euro area's peripheral debt, dropped 14 bps to 3.98%, with the spread between Italian and German 10-year yields slightly narrowing to 162 bps.

Greek government bonds were slightly underperforming their peers as the country heads into an election weekend.

Greece's 10-year yield dropped 10 bps to 3.62%, with the spread between German and Greek 10-year yields widening to 122 bps.

(Reporting by Stefano Rebaudo, editing by Emelia Sithole-Matarise)