* U.S. private employers add 135,000 jobs in May
* Service sector index rises to 53.7, but employment lower
* Rise in rates sends mortgage applications tumbling
* New factory orders rise 1 percent in April
* Unit labor costs fall 4.3 percent in first quarter
Hiring by U.S. firms was sluggish in May while a sharp rise in mortgage interest rates last week weighed on what has been a buoyant housing market, adding to signs the economy lost some momentum in the second quarter.
Indeed, a separate report from the Federal Reserve characterized the pace of the economic expansion as "modest to moderate" since mid-April as hiring remained relatively subdued.
The Fed's Beige Book of economic conditions is prepared as research for policymakers to use at their next meeting on June 18-19, a meeting that will be watched for any indications as to when the Fed may pull back on its stimulus program.
Private employers added 135,000 jobs in May, the ADP National Employment Report showed on Wednesday, an acceleration from April but missing forecasts for a gain of 165,000. April's private payrolls were revised to an increase of 113,000 from the previously reported 119,000 gain.
"The number was weak," said Mark Zandi, chief economist at Moody's Analytics, which jointly developed the report.
"The ADP (data) is suggesting instead of job growth stepping up, it's actually stepping down as we move into the summer months," Zandi told reporters. "It's not like we're falling off a cliff, it just feels like we're throttling back a little bit."
The ADP report showed manufacturers shed payrolls in May and a separate report indicated jobs growth in the vast services sector was weak last month, with a gauge of employment at services firms falling to its lowest in close to a year.
Economic growth is expected to cool in the current quarter from the 2.4 percent rate in the first three months of the year, partly due to fiscal belt-tightening in Washington. Economists still largely expect the recovery should regain traction in the second half of the year.
The goods producing sector cut 3,000 jobs in May, with a drop of 6,000 positions at manufacturing firms, which could be partially due to defense spending cutbacks, Zandi said.
Wall Street was down over 1 percent by mid-afternoon, while the weak data helped push Treasury debt prices higher. The dollar was weaker against a basket of currencies.
Activity in the U.S. services sector picked up slightly in May, with the Institute for Supply Management's services index edging up to 53.7 last month from 53.1 in April. That topped economists' expectations for 53.5.
A reading above 50 indicates expansion in the sector. The May figure was still off this year's peak of 56.0, which was hit in February.
The forward-looking new orders component rose but the employment measure slipped to the lowest level since last July at 50.1 from 52.0.
Even with the lackluster growth, the services industry held up better than its manufacturing counterpart, which contracted in May, according to data from ISM released earlier in the week.
Data on Wednesday added to signs of a slowdown in manufacturing as new orders for factory goods rose in April but not enough to reverse the prior month's plunge.
In a busy day for economic releases, yet another report showed unit labor costs fell in the first quarter by 4.3 percent, the most in four years, although the reading appeared to be distorted by a shift in employee compensation at the end of last year to avoid a tax hike.
FED IN FOCUS
The ADP figures come two days ahead of the government's more comprehensive labor market report, which includes both public and private sector employment.
That report is expected to show job growth increased only slightly, with nonfarm payrolls seen rising by 170,000 compared to the 165,000 seen in April.
The Fed's Beige Book on Wednesday said that hiring had increased at a "measured pace", though the regional details were mixed.
It also noted that wage and price pressures were contained, giving the Fed room to keep its aggressive use of monetary policy.
Friday's jobs figures will get even more scrutiny than usual with investors trying to gauge when the central bank may slow its current $85 billion a month bond-buying program, which is aimed at propping up the economic recovery.
"We have been seeing significant differences in ADP and nonfarm payrolls for months but regardless, it still doesn't suggest that the labor market is strong enough for the Fed to start tapering," said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co.
Since the report was revamped late last year, ADP's figures have missed the government's private payrolls numbers by an average 42,000 in either direction, according to High Frequency Economics.
"That 42,000 average miss for the past seven months is better than the 58,000 average in the prior seven months, although seven months of history is not conclusive," wrote Jim O'Sullivan, High Frequency Economics' chief U.S. economist.
Nervousness the Fed may taper bond purchases sooner than had been expected sent fixed 30-year mortgage rates up 17 basis points to average 4.07 percent in the week ended May 31, the Mortgage Bankers Association said.
Last week's interest rate was the highest since April 2012 and the first time rates have been above 4 percent since early May of last year.
Demand for refinancing was hit hardest by the acceleration in rates, with applications slumping 15.0 percent. The gauge of loan requests for home purchases - a leading indicator of home sales - held up relatively better, falling just 1.6 percent.