* US crude inventory data helps dilute OPEC impact
* Labor data encouraging; Friday's payrolls data awaited
* Apple drops on Goldman price target cut
* Indexes down: Dow 0.13 pct, S&P 0.17 pct, Nasdaq 0.06 pct (Adds details, changes quotes, updates prices)
By Yashaswini Swamynathan
June 2 (Reuters) - U.S. stocks clawed back some losses on Thursday morning as crude oil prices pulled back after data showed a drop in domestic stockpiles.
Oil prices had dropped about 2 percent earlier after the OPEC failed to reach a deal to freeze output, but the U.S. inventory data helped pare back losses to a fall of about 0.5 percent.
The S&P energy index was down 0.93 percent, with Exxon and Chevron both lower by more than 1 percent.
Data on Thursday showed U.S. private employers increased hiring in May and new applications for jobless benefits fell last week, further boosting the economic outlook for the second quarter.
While the labor data and Wednesday's factory data are encouraging, investors await the more comprehensive non-farm payrolls report on Friday for a better read into the health of the economy and to gauge when the Federal Reserve will raise rates.
"The bulk of the important data is going to be coming out tomorrow so markets tend to get relatively quiet, going into the sideways mode waiting for that," said Randy Frederick, managing director of trading and derivatives for Charles Schwab in Austin, Texas.
After the labor data was released, traders trimmed their expectations of a rate hike in June and raised their expectations of a hike in July, according to CME Group's FedWatch Tool.
At 11:15 a.m. ET the Dow Jones Industrial Average was down 22.36 points, or 0.13 percent, at 17,767.31.
The S&P 500 was down 3.5 points, or 0.17 percent, at 2,095.83 and the Nasdaq Composite was down 2.90 points, or 0.06 percent, at 4,949.35.
Seven of the 10 major S&P sectors were lower, led by the energy index.
Apple was down nearly 1 percent at $97.51 after Goldman Sachs cut its price target on the stock, citing lower growth expectations for the smartphone industry.
Mining equipment maker Joy Global rose 11.3 percent after signaling demand from China could improve. Larger rival Caterpillar was up 0.8 percent.
Oracle was down 4.8 percent at $38.34 after a former senior finance manager sued the company, claiming she was fired for complaining about improper accounting practices.
Declining issues outnumbered advancing ones on the NYSE by 1,574 to 1,260. On the Nasdaq, 1,313 issues rose and 1,299 fell.
The S&P 500 index showed 21 new 52-week highs and one new low, while the Nasdaq recorded 48 new highs and 13 new lows. (Reporting by Yashaswini Swamynathan in Bengaluru; Editing by Savio D'Souza)