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BEIJING, Dec 3 (Reuters) - China's services sector grew slightly faster in November, two surveys showed on Wednesday, a welcome respite to a run of underwhelming data but still unlikely to allay concerns about the softening Chinese economy.

The encouraging reports about the services sector, which creates more jobs than factories, contrasted sharply with data out on Monday that suggested growth in China's manufacturing industry slid to its lowest in at least six months in November.

That prompted some economists to predict that China would cut interest rates again in coming months after doing so unexpectedly on Nov. 21 to stoke growth in the world's second-largest economy.

"Things have gotten worse rather than better," said Louis Kuijs, an economist at RBS in Hong Kong, adding that any bottoming out in China's sagging housing market is unlikely to lead to a solid rebound next year.

"I predict one more rate cut to lower lending rates to 5.25 percent in the first quarter," he said.

The official non-manufacturing Purchasing Managers' Index, or PMI, rose to 53.9 in November from October's 53.8, well above the 50-point line that separates growth from contraction on a monthly basis.

A separate services PMI published by HSBC/Markit inched up to 53.0 last month from October's 52.9, as new orders rose at their quickest pace in 2-1/2 years.

But the surveys painted a mixed picture about the labour market, which Chinese leaders say is a crucial consideration when setting policy.

The official services PMI showed the labour market shrank for the fifth consecutive month in November as the employment sub-index hovered at 49.5, while the HSBC/Markit survey showed firms were still hiring as companies expanded their businesses.

Accounting for about 46 percent of China's economy last year, the services sector has weathered the growth slowdown better than factories, and authorities want it to overtake manufacturing as the bigger driver of activity in coming years.

FLAGGING GROWTH

Hurt by a sagging housing market, slowing domestic demand and investment and unsteady exports, China's economy is forecast by some analysts to be headed towards its worst slowdown in 24 years this year with annual growth seen at 7.4 percent.

Sources told Reuters after the rate cut that policymakers feared fourth-quarter growth could dip below 7 percent, despite a flurry of fiscal and monetary policy support measures earlier in the year.

In a sign that companies were feeling the drag of an unsteady economy, business expectations softened in both services PMIs.