* ISM non-manufacturing index up 56.5 vs est 53.3
* U.S. Treasury yields touch record low
* Dow down 0.16 pct, S&P down 0.09 pct, Nasdaq up 0.24 pct (Adds details, comments, updates prices)
By Yashaswini Swamynathan
July 6 (Reuters) - The S&P 500 and the Dow pared losses in late morning trade on Wednesday as robust economic data and recovering oil prices helped alleviate investor concerns about a global economic slowdown.
Nasdaq turned positive, helped by biotech stocks. Celgene's 4 percent rise gave the biggest boost to the index.
The pace of growth in the U.S. service sector increased in June was the fastest in seven months, according to an industry report released on Wednesday.
Brexit-related worries continued to weigh on the market and investors looked for safe havens. Gold rallied to a two-year high, while the benchmark 10-year U.S. Treasury yield touched a record low.
Major Asian and European indexes were lower. The British pound was at a 31-year low, while China allowed the value of the yuan to touch a 5-1/2 year low.
Global markets recovered some losses stemming from the Brexit vote last week, but weak economic data and worries over the fallout of the decision curtailed the rally.
"The selloff last week was an over reaction and the attempted rally was too fast and furious," said Art Hogan, chief market strategist at Wunderlich Equity Capital Markets.
"I think the compression of time and speed of the markets causes the pendulum to swing too far on every move we make."
U.S. Federal Reserve Governor Daniel Tarullo said world financial markets are well prepared for the impact of Brexit.
The Fed will release the minutes of its June meeting at 2:00 p.m. ET (1800 GMT). Traders will peruse the comments for clues on what the central bank thought the impact of Brexit would be.
Foreign exchange volatility and economic uncertainty after the Brexit vote have also imperiled a projected profit rebound in quarterly results in the United States. Second-quarter earnings are forecast to decline 3.9 percent from a year ago.
At 11:06 a.m. ET, the Dow Jones Industrial Average was down 28.46 points, or 0.16 percent, at 17,812.16.
The S&P 500 was down 1.96 points, or 0.09 percent, at 2,086.59.
The Nasdaq Composite was up 11.58 points, or 0.24 percent, at 4,834.49.
Eight of the 10 major S&P indexes were lower. Financials weighed on the index the most. Health was up 0.5 percent.
Data showed U.S. trade deficit widened more than expected to $41.1 billion in May as rising oil prices added to the import bill and exports remained constrained by a strong dollar. Economists had expected the trade gap to be about $40 billion.
Declining issues outnumbered advancing ones on the NYSE by 1,572 to 1,299. On the Nasdaq, 1,468 issues rose and 1,165 fell.
The S&P 500 index showed 40 new 52-week highs and three new lows, while the Nasdaq recorded 38 new highs and 41 new lows. (Reporting by Yashaswini Swamynathan in Bengaluru; Editing by Don Sebastian)