BEIJING, July 3 (Reuters) - Activity in China's services sector slowed to its lowest in five months in June, the HSBC/Markit Purchasing Managers' Index (PMI) showed on Friday, suggesting the economy still needs further policy support despite some signs of steadying.

The headline PMI for June fell to 51.8 from 53.5 in May, hitting the 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.

The 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.

"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 surveys bucked the findings of official factory and services surveys earlier this week.

The official factory survey showed activity expanded slightly in June while growth in the services sector sped up, offering some signs that the economy may be starting to slowly level out after a raft of support measures..

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.

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 Kevin Yao; Editing by Jacqueline Wong)