The rate of job losses at U.S. private employers slowed in December and the services sector showed marginal growth, according to reports on Wednesday which underlined the tentative nature of the economic recovery.

In the struggling housing sector, demand for mortgages held near six-month lows last week, according to a separate report.

The Institute for Supply Management said its services index rose to 50.1 in December, reaching above the 50 mark separating expansion from contraction for the third time in four months. The reading was above November's 48.7 but below economists' median forecast of 50.5.

The service sector...has been treading water since September, said Dan Greenhaus, chief economic strategist at Miller Tabak & Co in New York. Further improvement in this indicator and this sector is crucial for broader economic improvement.

Analysts also found only mild encouragement in ADP Employment Services data showing the private sector lost 84,000 jobs in December. That was fewer than the 145,000 jobs lost in November, but did exceed the 73,000 expected by economists.

In a separate report, global outplacement consultancy Challenger, Gray & Christmas, Inc. said planned layoffs at companies fell to the lowest in two years last month,

Wednesday's data on the job market did little to change expectations for Friday's U.S. Labor Department non-farm payrolls data for December. Economists forecast the U.S. lost 8,000 jobs overall last month, fewer than the 11,000 lost in November.

ADP was a touch weaker (than expected), but it still shows continued improvement in terms of the number of job losses, said Peter Boockvar, equity strategist at Miller Tabak & Co in New York.

Employers announced 45,094 planned job cuts last month, the fewest since December 2007, according to the Challenger report. That marked a 73 percent decline from 12 months ago, when 166,348 job cuts were reported, the report showed.

Last year marked the worst year of corporate job cuts since 2002, with employers announcing plans to cut 1,288,030 jobs. The pace of layoffs fell by 56 percent in the second half of the year however.

U.S. stocks stayed little changed after the release of the services data, while Treasury debt prices held steady at lower levels.

Meanwhile, a Mortgage Bankers Association survey showed demand for U.S. mortgages held near six-month lows last week as the highest long-term borrowing costs since August stifled refinancing,

Average 30-year mortgage rates jumped 0.10 percentage point to 5.18 percent in the January 1 week, up more than a half percentage point from the record low in March, driving down refinance requests to levels last seen in early August. The rate was last higher in late August at 5.24 percent.

Total mortgage applications eked out a 0.5 percent rise in the January 1 week after slumping nearly 23 percent in the Christmas week to the lowest level since late June.

In Europe, the fragility of the economic recovery was underlined on Wednesday by data from the European Union statistics office Eurostat showing industrial new orders in the 16 countries using the euro fell 2.2 percent in October against September. Economists polled by Reuters had on average expected a 1.1 percent monthly fall.

Orders were dragged lower mainly by a slump in volatile demand for ships, planes and trains, without which the monthly decline was only 0.4 percent.

Eurostat also said euro zone producer prices rose 0.1 percent in November against October, but were still 4.4 percent down year-on-year, emphasizing that inflationary pressures remained low. Economists polled by Reuters had on average expected a 0.2 percent monthly rise and a 4.5 percent year-on-year fall.

(Additional reporting by Ryan Vlastelica and Julie Haviv; Editing by Chizu Nomiyama)

Unemployment