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WRAPUP 3-U.S. services, factory data point to moderate economic growth

(Adds details from ISM report, analyst comments, updates markets)

* ISM services sector index falls in May

* Factory orders slip 0.2 percent in April

* First-quarter productivity revised up to show it unchanged

WASHINGTON, June 5 (Reuters) - U.S. services sector activity slowed in May as new orders tumbled, but a jump in employment to a near two-year high pointed to sustained labor market strength despite a deceleration in job growth last month.

The moderation in services industries production, together with other data on Monday showing orders for manufactured goods falling in April for the first time in five months and worker productivity unchanged in the first quarter, suggest limited scope for faster economic growth.

"The economy is neither accelerating nor slowing, but the labor market is looking up," said Joel Naroff, chief economist at Naroff Economic Advisors in Holland, Pennsylvania.

The Institute for Supply Management (ISM) said its non-manufacturing activity index fell six-tenths of a percentage point to a reading of 56.9. A reading above 50 indicates expansion in the sector, which accounts for more than two-thirds of U.S. economic activity.

Services industries reported a 5.5 percentage points dive in new orders last month. Prices paid by non-manufacturing industries for materials and services declined after increasing for 13 straight months.

But a measure of services sector employment surged 6.4 percentage points to its highest level since July 2015, suggesting labor market strength even as nonfarm payrolls increased 138,000 in May after rising 174,000 in April.

The drop in prices paid by services industries could attract attention from some Federal Reserve officials when they meet on June 13-14 to deliberate on monetary policy.

The U.S. central bank is expected to raise its benchmark overnight interest rate by 25 basis points at that meeting after a similar increase in March.

GRADUAL RATE HIKES

"Most inflation comes from services rather than goods sitting on store shelves, so if services prices are in decline, the Fed has little hope of achieving its 2 percent inflation objective," said Chris Rupkey, chief economist at MFUG in New York.

"We will see if this alters their gradual pace of rate hikes later on this year when they provide their latest interest rate forecasts at the upcoming meeting."

U.S. stocks were trading lower, while the dollar rose against a basket of currencies. Prices for U.S. Treasuries fell.

In a separate report on Monday, the Commerce Department said factory goods orders dropped 0.2 percent in April after jumping 1.0 percent in March. Orders rose 4.4 percent from a year ago.

Manufacturing, which accounts for about 12 percent of the U.S. economy, is being supported by a recovery in the energy sector that has led to demand for oil and gas drilling equipment.

"The slow growth narrative for the manufacturing sector and business spending outlook remains intact," said Tim Quinlan, a senior economist at Wells Fargo Securities in Charlotte, North Carolina.

A third report from the Labor Department showed nonfarm productivity, which measures hourly output per worker, was unchanged in the last quarter. It was previously reported to have declined at a 0.6 percent annualized pace.

Productivity has increased at an average annual rate of 0.6 percent over the last five years, below its long-term rate of 2.1 percent from 1947 to 2016, indicating that the economy's potential rate of growth has declined.

Economists blame low capital expenditure, which they say has resulted in a sharp drop in the capital-to-labor ratio, for the weakness in productivity. There are also perceptions that productivity is being inaccurately measured, especially on the information technology side.

"The result is an economy that is still stuck on a shallow growth track," said Steven Ricchiuto, chief U.S. economist at Mizuho in New York.

(Reporting by Lucia Mutikani; Editing by Andrea Ricci)