* 158,000 private jobs added in June vs. est. 185,000 -ADP
* Weekly jobless claims rise for third straight week
* Tesla slips after Model S fails to ace some tests
* Indexes down: Dow 0.42 pct, S&P 0.58 pct, Nasdaq 0.88 pct (Adds details, changes comment, updates prices)
July 6 (Reuters) - U.S. stocks fell in late morning trading on Thursday as weak jobs data from the private sector struck a bleak tone for the critical nonfarm payrolls report due on Friday, while investors fretted about rising tension in the Korean peninsula.
The ADP National Employment Report showed private employers added 158,000 jobs in June, below the estimated addition of 185,000, suggesting some cooling in the labor market as it nears full employment.
The report by payrolls processor ADP acts as a precursor to monthly nonfarm payrolls data, which includes hiring in both the public and private sectors.
"The market moves significantly on the jobs report. We are expecting to see a little bit of a rebound from last month, but again we didn't get that in the ADP number today which was also expected to be stronger than what it was," said Lindsey Bell, investment strategist at CFRA Research.
Another set of data showed weekly jobless claims rose for the third straight week, with claims climbing to 248,000, above the 243,000 expected.
Bell said ongoing geopolitical worries around North Korea were also adding to the pressure.
The United States said it was ready to use force if need be to stop North Korea's nuclear missile program after the country test launched a ballistic missile that could hit Alaska.
At 11:01 a.m. ET (1501 GMT), the Dow Jones Industrial Average was down 90.49 points, or 0.42 percent, at 21,387.68 and the S&P 500 was down 14.19 points, or 0.58 percent, at 2,418.35.
The Nasdaq Composite was down 53.86 points, or 0.88 percent, at 6,097.00.
All the 11 major S&P 500 sectors were lower, with the tech sector's 0.97 percent fall topping the list.
A fall in Apple and Microsoft weighed the most on the S&P and the Nasdaq.
Investors are also parsing minutes from the Federal Reserve's last meeting that showed policymakers were increasingly split on the outlook for inflation and how it might affect the future pace of interest rate hikes.
The Fed's preferred measure of underlying inflation slipped to 1.4 percent in May and has run below the 2 percent target for more than five years now.
Shares of Tesla fell 4.6 percent after the luxury electric carmaker's Model S did not get the top score in certain tests by the Insurance Institute for Highway Safety.
General Electric slipped 1.7 percent after the European Commission accused the company of providing misleading information during a merger deal. The stock was among the top three drags on the S&P.
HSN jumped 27 percent after Liberty Interactive said it would buy the remaining 62 percent stake in the TV shopping network.
Declining issues outnumbered advancers on the NYSE by 2,138 to 630. On the Nasdaq, 1,996 issues fell and 655 advanced. (Reporting by Tanya Agrawal in Bengaluru; Editing by Anil D'Silva)