(Updates to afternoon U.S. trading)

* Wall Street stocks mixed

* Euro STOXX fall after July gain of 2%

* US job openings still elevated

* Euro zone and China factory data suggests economic weakness

* Oil slips from three-month high

* Dollar advances again versus yen

Aug 1 (Reuters) - Global stocks were mostly down and oil slipped on Tuesday as declining factory activity in the euro zone and China tempered investors' optimism over U.S. economic prospects and a likely end to Fed rate hikes.

Markets also digested fresh U.S. manufacturing data, which appeared to stabilize at weaker levels in July amid a gradual improvement in new orders. Other data showed U.S. job openings fell to the lowest level in more than two years in June, but remained at levels consistent with tight labour market conditions.

On Wall Street, the Dow Jones Industrial Average was virtually flat at 35,579. The S&P 500 lost 0.28%, to 4,576 and the Nasdaq Composite dropped 0.34%, to 14,297.

Shares of Merck & Co. dipped 0.5% even though it raised its full-year profit forecast; Pfizer missed estimates for quarterly revenue, sending shares down 0.6%; and Caterpillar Inc rose 8% after reporting a better than expected rise in second-quarter profit, although it also warned on third-quarter sales and margins.

European stocks fell 0.9%, stepping back from a 2% increase in July, the index's second month of gains.

UK stocks also fell 0.4%, though HSBC climbed 1.3% after announcing a $2 billion share buyback and raising its key profitability target.

Losses accelerated across European markets after data showed manufacturing activity in the bloc contracted in July at the fastest pace since May 2020 amid slumping demand even as factories cut their prices sharply.

The data disappointed investors who are readying for an end to a series of U.S. Federal Reserve interest rate hikes, with an increase last week widely seen as one of the last in its current tightening cycle.

Market players put Tuesday's losses down to a combination of profit taking at the start of the month, as well as nerves over the health of the global economy.

"The economy is a little bit weaker than perhaps people would like, and I think that's a concern for earnings growth heading into the second half of the year," said Michael Hewson, chief market analyst at CMC Markets.

U.S. Treasury yields rose on Tuesday as investors positioned for the Treasury's refunding announcement on Wednesday and anticipated more economic resilience going forward, despite data on Tuesday showing a slowdown in activity.

The yield on 10-year Treasury notes was up 9.4 basis points at 4.051%. The two-year yield, which typically moves in step with interest rate expectations, was up 3 basis points at 4.904%.

COMMODITIES DIP

Oil prices edged lower on a stronger dollar and signs of profit-taking, after a rally in July when investors bet on tighter global supplies and demand growth in the second half of 2023.

U.S. crude fell 0.44% to $81.44 per barrel and Brent was at $85.01, down 0.49% on the day.

Energy giant BP fell 0.25% and boosted its dividend by 10% after reporting a second-quarter profit of $2.6 billion, down 70% from a year earlier.

Gold prices fell over 1% on Tuesday, weighed down by a stronger dollar and an uptick in bond yields, while investors looked forward to more U.S. economic data this week that could influence the Federal Reserve's policy stance.

DOLLAR VS YEN

The U.S. dollar index, which measures the currency against six major peers, rose 0.47% to as high as $102.37 for the first time since July 10.

The dollar also hit a three-week high against the yen as investors continued to seek clarity on the Bank of Japan's recent adjustment to its yield curve control and what that might mean for monetary policy.

China's stumbling post-pandemic recovery remained in focus, for instance, after a surprise contraction in manufacturing in a private-sector survey released Tuesday.

MSCI's broadest index of Asia-Pacific shares traded down about 0.5%, slightly below the high reached Monday, which was its strongest since April last year.

Still, many investors remain positive.

"Markets are fully focusing on the bright side of the puzzle," said Sandrine Perret, portfolio manager at Unigestion. "The market reaction since last week, after the Fed rally, has been really strong and resilient."

(Reporting by Lawrence Delevingne in Boston, Tom Wilson in London and Kevin Buckland in Tokyo; Editing by Angus MacSwan and Susan Fenton)