LONDON, Sept 21 (Reuters) - Euro zone bond yields rose on Thursday to multiple-month highs after the Federal Reserve kept rates unchanged, projected another rate hike by year end and much tighter monetary policy through 2024 than previously expected.

The focus of investors remained on central banks with rate-setting meetings on Thursday in Britain, Norway, Sweden and Switzerland.

The Fed's benchmark overnight interest rate may still be lifted one more time this year to a peak 5.50%-5.75% range, according to updated quarterly projections released by the U.S. central bank, and rates will be kept significantly tighter through 2024 than previously expected.

Mirroring a rise in U.S. Treasury yields, Germany's 10-year government bond yield rose, to touch a fresh six-month high. The yield moves inversely to the price.

It was last up 2.8 basis points (bps) to 2.73%, after touching its highest since early March.

The German 2-year bond yield, which is sensitive to changes in interest rate expectations, was 2.7 bps higher at 3.28%, after hitting its highest since mid July.

"We still think that the Fed is done with rate hikes. The bar for another hike in November is high and data would have to surprise significantly to the upside for the Fed to hike again," said Mohit Kumar, rate strategist at Jefferies.

"Our pecking order of duration preference would be Gilts, Bunds and (U.S. Treasuries) as in the first two cases, there are clearer indications that the central banks are done," he added.

The European Central Bank raised interest rates last week and will next set interest rates in late October. Investors think borrowing costs will stay at 4%, according to pricing in derivatives markets.

CENTRAL BANKS IN ACTION

The Bank of England (BoE) meeting later in the day will be closely watched after Britain's high inflation rate unexpectedly slowed, raising the prospect of the BoE pausing its long run of interest rate hikes.

"Any dovish signal by the BoE, or even a decision to remain on hold, would contribute to reinforcing market sentiment across fixed income," said UniCredit strategists in a note to clients.

Britain's 10-year gilt yield rose 3.5 bps to 4.25% after falling on Wednesday to its lowest since July.

Italy's 10-year bond yield was last up 5.1 bps to 4.50%.

The Swiss National Bank held its policy interest rate unchanged at 1.75% on Thursday, marking the first time the central bank has not hiked rates since March 2022.

While Sweden's central bank raised its key policy rate by a quarter percentage point to 4.00% as expected on Thursday and said it might need to do more to bring inflation back to its 2% target. (Reporting by Joice Alves Editing by Gareth Jones)