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WRAPUP 1-U.S. private hiring slows in June, weekly jobless claims rise

* Private payrolls increase 158,000 in June

* Weekly jobless claims rise 4,000

* Trade deficit declines 2.3 percent in May

WASHINGTON, July 6 (Reuters) - U.S. private employers hired fewer workers than expected in June and applications for unemployment benefits last week increased for a third straight week, suggesting some cooling in the labor market as it nears full employment.

The ADP National Employment Report showed on Thursday that private sector payrolls increased by 158,000 jobs last month, stepping down from the 230,000 positions created in May and below economists' expectations for a gain of 185,000.

The report, jointly developed with Moody's Analytics, came ahead of the Labor Department's more comprehensive non-farm payrolls report on Friday, which includes both public and private-sector employment.

According to a Reuters survey of economists, nonfarm payrolls likely increased by 179,000 last month after May's 138,000 gain. The unemployment rate is forecast unchanged at 4.3 percent.

The ADP report has a spotty record predicting nonfarm payrolls, but June's modest job gains together with a steady rise in first-time applications for jobless benefits could raise concerns that the labor market is losing some momentum.

In a separate report, the Labor Department said initial claims for state unemployment benefits increased 4,000 to a seasonally adjusted 248,000 for the week ended July 1. It was the third straight weekly increase in claims.

Claims rose last week likely as some automakers closed assembly plants for the annual summer retooling. Still, it was the 122nd straight week that claims remained below 300,000, a threshold associated with a healthy labor market.

That is the longest such stretch since 1970, when the labor market was smaller. The labor market is near full employment, with the jobless rate at a 16-year low.

The four-week moving average of claims, considered a better measure of labor market trends as it irons out week-to-week volatility, rose 750 to 243,000 last week.

Unadjusted claims for Michigan, a hub for auto production, increased 1,159 last week.

Automakers normally shut assembly plants for annual retooling at the start of July, which tends to push up claims.

Applications are likely to remain elevated as some companies like General Motors embark on extended summer shutdowns to deal will slower sales, which have led to an inventory bloat.

Motor vehicle manufacturers reported on Monday that auto sales fell in June for a fourth straight month. Even before the annual summer plant closures, automakers have been laying off workers in response to the softening demand.

Thursday's claims report also showed the number of people still receiving benefits after an initial week of aid increased 11,000 to 1.96 million in the week ended June 24. The so-called continuing claims have now been below 2 million for 12 straight weeks, pointing to diminishing labor market slack.

The four-week moving average of continuing claims rose 6,750 to 1.94 million, remaining below the 2 million mark for 10 consecutive weeks.

A third report from the Commerce Department on Thursday showed the trade deficit fell 2.3 percent to $46.5 billion in May.

When adjusted for inflation, the trade deficit narrowed to $62.8 billion from $63.8 billion in April. Real goods exports surged to an all-time high in May, propelled by record high petroleum exports.

Still, the real trade deficit averaged $63.3 billion in April and May, above the first quarter's average of $62.2 billion. That suggests trade will be a drag on gross domestic product in the second quarter after contributing 0.23 percentage point to the economy's 1.4 percent annualized growth pace in the first three months of the year.

The Atlanta Federal Reserve is forecasting GDP rising at a 3.0 percent rate in the second quarter.

(Reporting by Lucia Mutikani; Additional reporting by Richard Leong in New York; Editing by Andrea Ricci)