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GLOBAL MARKETS-Equities weaken after Dow breaks 22,000; dollar soft

* Apple shares hit all-time top after results

* Dow Jones Industrials breaks 22,000 mark

* Dollar holds at 15-month lows (Updates with U.S. market open, changes byline, dateline; previous LONDON)

NEW YORK, Aug 2 (Reuters) - World stock markets fell on Wednesday even as Wall Street's key Dow Jones Industrial Average broke the 22,000 barrier on strength in Apple shares, while the U.S. dollar fell to near 15-month lows on doubts about another rate hike this year.

Shares of Apple, the largest U.S. company by market capitalization, surged 4.9 percent to a record high of $159.75 in the wake of its earnings, helping lift the Dow above the key 22,000 mark.

Apple reported better-than-expected iPhone sales, revenue and earnings per share and signaled its upcoming 10th-anniversary phone is on schedule.

But Apple's gains were not enough to prop up the broader U.S. stock indexes, with the benchmark S&P 500 and Nasdaq both lower.

"Round numbers are a focal point, they are kind of arbitrary but people seem to focus and it can affect sentiment," said Brian Jacobsen, senior investment strategist at Wells Fargo Funds Management in Menomonee Falls, Wisconsin.

"If theres going to be something that gives the market more fuel it has to come from fundamentals. Excitement about a round number can only carry it so far."

The Dow Jones Industrial Average rose 40.21 points, or 0.18 percent, to 22,004.13, the S&P 500 lost 4.96 points, or 0.20 percent, to 2,471.39 and the Nasdaq Composite dropped 29.78 points, or 0.47 percent, to 6,333.16.

The pan-European FTSEurofirst 300 index lost 0.46 percent and MSCI's gauge of stocks across the globe shed 0.13 percent.

European shares were weighed down by declines in banking and mining shares.

The U.S. dollar hit its lowest level against the euro in more than 2-1/2 years on Wednesday on doubts about another Federal Reserve interest rate increase this year and expectations for European Central Bank hawkishness.

Tepid U.S. inflation along with political turmoil in Washington has lessened the possibility of another Federal Reserve rate hike this year.

Improving data in other major economies has also served to push the greenback down nearly 11 percent from January highs, benefiting commodities and emerging markets.

The dollar index fell 0.27 percent, after touching 92.734, the lowest since early May 2016. the euro up 0.49 percent to $1.1859.

Investors also dealt with conflicting statements from Federal Reserve officials.

St. Louis Federal Reserve James Bullard is opposed to further U.S. interest rate increases by the central bank and warned that more hikes could hinder domestic inflation from achieving the Fed's 2-percent goal, Market News International reported.

But Cleveland Fed President Loretta Mester said the Fed should remain focused on gradually tightening U.S. policy because one-off factors, not a long-lasting trend, have caused inflation to weaken in recent months.

U.S. private employers added 178,000 jobs in July, below economists' expectations, a report by a payrolls processor showed on Wednesday, ahead of the U.S. Labor Department's more comprehensive non-farm payrolls report on Friday.

U.S. profits for the second quarter have been strong, with earnings growth currently at 11.4 percent, according to Thomson Reuters data. Of the 350 companies in the S&P 500 that have reported through Wednesday morning, 70 percent have topped expectations.

Benchmark 10-year notes last rose 1/32 in price to yield 2.2496 percent, from 2.251 percent late on Tuesday.

U.S. crude rose 0.53 percent to $49.42 per barrel and Brent was last at $52.17, up 0.75 percent on the day.

(Additional reporting by Rodrigo Campos; Editing by Bernadette Baum)