U.S. equities closed higher on Thursday, the first trading day in June, as Wall Street got ready for the release of the monthly jobs report.

The Nasdaq composite gained about 0.8 percent, hitting intraday and record highs. The S&P 500 also rose nearly 0.8 percent to notch all-time highs, with materials, financials and health care leading advancers. The health care sector also reached its first 52-week high since March 15.

The Dow Jones industrial average rose about 135 points, with UnitedHealth and Goldman Sachs contributing the most gains. The 30-stock index also traded about 25 points away from its intraday record.

Economists polled by Reuters expect the U.S. economy to have added 185,000 jobs last month. But David Kelly, chief global strategist at JPMorgan Funds, said expectations may have increased in the market after a strong report from ADP and Moody's Analytics.

The Thursday report said private payrolls surged by 253,000 in May, easily topping a consensus estimate of 185,000.

"It was a very good, positive surprise. We've had a few negative surprises, so this is definitely against the current," said JPMorgan Funds' Kelly. "Overall, it says the economy is still moving along nicely."

The report from ADP and Moody's is often seen as a preview to the U.S. government's nonfarm payrolls report, which is set for release Friday at 8:30 a.m.

"What the ADP number does is it raises expectations that the jobs report can come at the top end of the range and maybe above the estimate," said JJ Kinahan, chief market strategist at TD Ameritrade.