* U.S. crude inventory data offsets OPEC impact
* Labor data encouraging; Friday's payrolls data awaited
* Apple drops on Goldman price target cut
* Indexes down: Dow 0.12 pct, S&P 0.18 pct, Nasdaq 0.19 pct (Updates to early afternoon)
By Yashaswini Swamynathan
June 2 (Reuters) - U.S. stocks were lower in afternoon trading on Thursday, having clawed back most of their losses after crude oil prices turned course to trade higher.
Oil prices were up about 0.5 percent after data showed a weekly drawdown in U.S. crude stockpiles. Crude had dropped about 2 percent earlier on OPEC's failure to reach a deal to freeze output.
Crude prices' reversal helped the S&P energy index cut its losses to 0.76 percent, from 1 percent, and surrender its position as the biggest drag on the S&P 500. Exxon and Chevron stayed lower by more than 0.7 percent.
Separately, 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 interest 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 12:23 p.m. ET (1623 GMT) the Dow Jones Industrial Average was down 20.99 points, or 0.12 percent, at 17,768.68.
The S&P 500 was down 3.84 points, or 0.18 percent, at 2,095.49 and the Nasdaq Composite was down 9.34 points, or 0.19 percent, at 4,942.91.
Seven of the 10 major S&P sectors were lower, now led by the utilities index's 0.64 percent drop.
The healthcare index's 0.72 percent rise was the highest among gainers, helped by Johnson & Johnson. J&J rose 1 percent after agreeing to buy a hair products maker.
Apple was down 1.2 percent at $97.29 after Goldman Sachs cut its price target on the stock, citing lower growth expectations for the smartphone industry. The stock was the biggest drag on all three indexes.
Joy Global rose 11.8 percent, and was the biggest percentage gainer on the NYSE, after the mining equipment maker signaled demand from China could improve. Larger rival Caterpillar was up 1.3 percent.
Oracle was down 5.1 percent at $38.21 after a former finance manager sued the company, claiming she was fired for complaining about improper accounting practices.
Declining issues outnumbered advancing ones on the NYSE by 1,528 to 1,368. On the Nasdaq, 1,390 issues rose and 1,294 fell.
The S&P 500 index showed 22 new 52-week highs and one new low, while the Nasdaq recorded 53 new highs and 14 new lows. (Reporting by Yashaswini Swamynathan in Bengaluru; Editing by Savio D'Souza)