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* June services PMI at 51.8, lowest since January

* Employment sub-index weakest in 3 months

* Weak manufacturing, slowing services seen prompting stimulus

By Kevin Yao

BEIJING, July 3 (Reuters) - Activity in China's services sector slowed to its lowest in five months in June, a private survey showed on Friday, suggesting the economy still needs further policy support despite some signs of steadying.

Beijing has rolled out a suite of measures since last year, including interest rate cuts, to prop up growth, but economists worry that persistent weakness in exports and the property sector combined with high local government debt will keep the world's second-largest economy under pressure.

The headline HSBC/Markit Purchasing Managers' Index (PMI) for June fell to 51.8 from 53.5 in May, hitting its lowest since January but still indicating expansion for the 11th straight month.

A reading above 50 points indicates growth on a monthly basis, while one below that points to contraction.

The new business sub-component fell to 52.2, an 11-month low, from 54.4 in May, while the employment sub-index fell to its lowest in three months and indicated jobs were being shed.

"In the service sector, business activity, new orders and employment all expanded at slower rates, while optimism towards the business outlook also moderated," said Annabel Fiddes, an economist at Markit.

A similar HSBC/Markit factory survey released on Wednesday showed activity contracted for the fourth straight month in June but at a slower pace than in May, fueling hopes that that sector may be slowly bottoming out.

"The persistently weak performance of manufacturers combined with a slowdown in the service sector is likely to prompt the authorities to introduce further stimulus measures to ensure growth momentum improves in the second half of the year and to reach the GDP growth target of around 7 percent," Fiddes said.

The HSBC readings bucked the findings of official factory and services surveys earlier this week, pointing to growing uneveness in conditions even for companies competing in the same sectors.

The official factory survey showed activity expanded slightly in June while growth in the services sector sped up. .

The official surveys focus on large, state-owned firms, and the private ones on small and mid-sized companies which are facing tougher financial and operating conditions.

Growth in China's services companies has been more resilient than at its ailing factories, but the sector had shown signs of succumbing to the broader economic cooldown in recent months.