(Refiles to add GLOBAL MARKETS to headline; fix story title; wrapup number)

* European shares fall, Asian stocks at 2021 lows

* Bitcoin jumps on short-covering, Amazon speculation

* Govt bond yields post sizable drop

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

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

NEW YORK/LONDON, July 26 (Reuters) - U.S. stocks slipped from record highs on Monday and the dollar softened as investors cashed in on recent gains and turned their focus to the Federal Reserve's policy meeting, starting Tuesday, for clues on the outlook for monetary policy.

But declines in U.S. shares were slim compared with losses in Asia overnight, when MSCI's broadest index of Asia-Pacific shares outside Japan slumped 2.1% to its lowest since December, hurt by concerns over tighter regulations in China.

In the United States, investors will closely parse comments by Federal Reserve Chair Jerome Powell on how the central bank will start tapering its asset purchases and any remarks he might make about the future of interest rates.

By late morning, U.S. shares were vacillating between modest gains and losses. The Dow Jones Industrial Average was flat at 35,062.39, the S&P 500 edged up 0.06% to 4,414.67, and the Nasdaq Composite edged 0.04% lower to 14,830.320.

"Powell will likely highlight that the recovery is on track but COVID remains a key downside risk," analysts at Bank of America said in a note, adding that he will probably signal that any details about the Fed's tapering of asset purchases will be revealed in future meetings.

In a sign that risk appetite remained firm on Wall Street, bitcoin, the world's biggest cryptocurrency and sometimes an indicator of the demand for risk, soared 8.3% to $38,371.80 while ether jumped 6.35% to $2,333.26.

Speculation that online retailing giant Amazon might accept bitcoin as payment sparked the latest rally, and short sellers covering their positions added to the surge.

On the other hand, the U.S. dollar, which usually benefits when investors are seeking safety, softened as investors turned their attention to the Fed meeting.

The dollar index lost 0.36% to 92.569 against a basket of six major currencies, but was not far off a 3-1/2-month high of 93.194 struck last week.

The dollar has gained nearly 4% from a low on May 25 as an improving U.S. economy bolstered the outlook for the Fed to start paring asset purchases as early as this year.

Indeed, investors have been pulling money out of Asian and emerging market stocks and adding to their U.S. holdings, attracted by forecast-beating earnings and a recovery in the U.S. economy.

Bond markets have remained remarkably untroubled by the prospect of eventual tapering. Yields on U.S. 10-year notes US10YT=RR have fallen for four weeks in a row - they slipped to a low of 1.221% on Monday before edging back up to 1.2779%.

But the drop in Treasury yields has done little to undermine the dollar, in part because European yields have fallen even further amid expectations of continued massive bond-buying by the European Central Bank.

Gold prices were subdued as investors stayed on the sidelines ahead of the Federal Reserve meeting, while oil prices weakened a touch, after having been buoyed by views that demand will remain strong as the global economy gradually opens and supply stays tight.

Brent slid 0.07% to $74.03 a barrel, while U.S. crude declined 0.47% to $71.73.

(Additional reporting by Wayne Cole in Sydney and Dhara Ranasinghe in London; Editing by Nick Macfie, Alex Richardson and Dan Grebler)