(Recasts lead with Fed statement, adds comment in paragraphs 5-6, 10-11, updates prices at 3:25 p.m.)

* Fed projects rates to remain higher for longer

* Global equities waver as investors assess policy outcome

* Oil prices fall, dollar strengthens

* Graphic: World FX rates http://tmsnrt.rs/2egbfVh

* Graphic: Global asset performance http://tmsnrt.rs/2yaDPgn

NEW YORK, Sept 20 (Reuters) - A gauge of global equities wavered and shorter-dated Treasury yields edged up on Wednesday after the Federal Reserve projected another rate hike by year end and monetary policy significantly tighter through 2024 than previously expected.

The U.S. central bank held interest rates steady as expected at the end of a two-day policy meeting, but the policy-setting Federal Open Market Committee said "inflation remains elevated" and Fed Chair Jerome Powell said the Fed's job is to lower it.

"We are committed to achieving and sustaining sufficiently restrictive policy to bring inflation down to 2% over time," Powell said at a press conference.

Fed officials now see the personal consumption expenditures price index at 3.3% at year end, up from June's forecast of 3.2%, and its overnight lending rate to be 5.1% at the end of 2024, about 50 basis points higher than futures have projected.

"The Fed is trying to send as hawkish a signal as it possibly can. It's just a question of whether the markets will listen to them without taking them with a grain of salt," said Gennadiy Goldberg, head of U.S. interest rate strategy at TD Securities in New York.

"They're talking about higher rates for longer, but it's really the economy that matters. And if the economy starts to soften, I don't think these dot plot projections will actually hold up."

The yield on two-year Treasuries, which reflect interest rate expectations, rose 3.5 basis points to 5.144% as the futures priced in the Fed's overnight rate staying above 5% through September 2024 - further out than previously projected.

The yield on the benchmark 10-year note fell 1.6 basis points to 4.351% after hitting 4.371% on Tuesday, the highest since late 2007, a sign that yield curve remains firmly inverted and is heralding a recession ahead.

MSCI's U.S.-centric gauge of stocks across the globe fell 0.25% as stocks on Wall Street mostly slid.

"Right now the message is we're going to leave rates higher for longer to make sure we slay the inflation dragon. That means less rate cuts in 2024," said Anthony Saglimbene, chief market strategist at Ameriprise Financial in Troy, Michigan.

"This last leg might be a little bit more difficult, and so they're going have to navigate the message around staying higher for longer while trying to engineer that soft landing."

The reaction on Wall Street was choppy. The Dow Jones Industrial Average rose 0.23%, the S&P 500 lost 0.42% and the Nasdaq Composite dropped 0.84%.

Earlier in Europe, the pan-regional STOXX 600 index rose 0.91%. MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.5% and Japan's Nikkei fell 0.7%.

The Fed leads a week jammed with key central bank meetings, with policy announcements in Sweden, Switzerland, Norway, Britain and Japan all due later this week.

Sterling came under pressure after data showed Britain's high inflation rate fell unexpectedly in August, prompting speculation that the Bank of England could pause its historic run of interest rate hikes as soon as Thursday.

The dollar index rose 0.076%, with the euro down 0.02% to $1.0675.

Japan's yen continued to face pressure, prompting a riposte from Japan's top financial diplomat.

The yen is down 11% on the dollar this year as expectations firm for U.S. rates to stay high and Japanese rates to stay low, earlier hitting a 10-month trough of 148.17 per dollar.

Benchmark 10-year Japanese government bonds are at 0.72%, but have been creeping toward the Bank of Japan's adjusted tolerance for yields 1% either side of zero.

Rising yields have kept a lid on gold prices, with spot gold last trading at $1,930 an ounce.

Oil prices fell about 1% to a one-week low the Fed stiffened its hawkish stance.

Brent futures for November delivery fell 81 cents, or 0.9%, to settle at $93.53 a barrel, while U.S. West Texas Intermediate crude (WTI) for October delivery fell 92 cents, or 1.0%, to settle at $90.28.

Gold slightly pared gains after the Fed statement. U.S. gold futures settled 0.7% higher at $1,967.10.

(Reporting by Herbert Lash, reporting by Dhara Ranasinghe and Samuel Indyk in London, Tom Westbrook in Singapore; Editing by Toby Chopra, Chizu Nomiyama, Sharon Singleton and Aurora Ellis)