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* US private payrolls beat expectations in June

* Energy, consumer discretionary sectors slump

* Exxon shares drop as co signals sharp drop in profit

(Updates with close of US market)

July 6 (Reuters) - Wall Street's main indexes ended lower on Thursday in a broad selloff after data showing a strong labor market boosted bond yields and fanned fears the Federal Reserve will be aggressive in raising U.S. interest rates.

Private payrolls surged far more than expected in June, data showed, suggesting the labor market remained on solid ground despite growing risks of a recession. A separate report showed U.S. job openings dropped in May, but remained at higher levels.

A day before the monthly U.S employment report, evidence of a solid labor market spurred expectations the Fed will keep interest rates higher for longer to tame inflation that remains above its target.

“We don’t see any softening in the labor market,” said Brad McMillan, chief investment officer for Commonwealth Financial Network. “The Fed doesn’t have to worry about the jobs market. When you look at their mandate, they have no reason not to keep hiking and to keep hiking for a while.”

According to preliminary data, the S&P 500 lost 35.41 points, or 0.80%, to end at 4,411.41 points, while the Nasdaq Composite lost 113.64 points, or 0.82%, to 13,678.01. The Dow Jones Industrial Average fell 370.90 points, or 1.08%, to 33,917.74.

Energy and consumer discretionary were among the biggest declining S&P 500 sectors.

Treasury yields jumped following the labor market data. The benchmark 10-year yield burst above 4% while the two-year Treasury yield, which typically moves in step with interest rate expectations, hit a 16-year high.

U.S. interest rate futures saw an increased probability of another rate hike by the Federal Reserve in November, according to CME's FedWatch.

The Fed did not hike rates at its June meeting but is widely expected to resume increases at its meeting later this month. Dallas Fed President Lorie Logan said there was a case for a rate rise at the June policy meeting.

In company news, Exxon Mobil Corp shares fell after the oil major signaled second-quarter operating profits fell sharply on lower natural gas prices and weaker oil refining margins.

Second-quarter corporate reports will arrive in the coming weeks with S&P 500 earnings expected to fall 5.7% from the year-ago period, according to Refinitiv data.

“You have a situation where rates are going higher, profits are not really moving," said King Lip, chief strategist at Baker Avenue Wealth Management. "That’s usually not a good combination for stocks.”

JetBlue Airways shares dropped a day after the company said it would follow a U.S. judge's May order to end its alliance with American Airlines to protect a planned purchase of Spirit Airlines. (Reporting by Lewis Krauskopf in New York, Bansari Mayur Kamdar and Johann M Cherian in Bengaluru; Editing by Vinay Dwivedi, Shinjini Ganguli and David Gregorio)