BEIJING, Oct 1 (Reuters) - Growth in China's services industry steadied in September, an official survey showed on Thursday, helping offset persistent weakness in manufacturing which has been weighing heavily on the world's second-largest economy.

The services industry has been the lone bright spot for the economy in the last few years, helping to cushion a prolonged downturn in the factory sector, but it too has begun to show signs of fatigue in recent months as consumers grow more cautious.

The official non-manufacturing Purchasing Managers' Index (PMI) stood at 53.4, the same pace as in previous month, according to the National Bureau of Statistics (NBS).

A reading above 50 points indicates an expansion in activity on a monthly basis, while one below that points to a contraction.

China's economy is gradually slowing from a breakneck double-digit pace in past decades, as Beijing tries to reform its growth model from a reliance on heavy manufacturing and exports to one with a more vibrant services sector.

However, a spate of weak data in recent months and company warnings of slowing sales have fueled fears it is at risk of a harder landing, roiling global financial markets.

The government expects economic growth to ease from 7.3 percent in 2014 to 7 percent in 2015, which would mark the slowest rate in a quarter of a century.

A slump in financial services activity following this summer's stock market crash could put a further dent in that.

Some economists believe current growth levels are already much weaker than official data suggest.

The services sector has accounted for the bigger part of China's economic output for at least two years, with its share rising to 48.2 percent last year, compared with the 42.6 percent contribution from manufacturing and construction.

(Reporting by Winni Zhou, Xiaoyi Shao and Kevin Yao; Editing by Kim Coghill)