BEIJING, July 1 (Reuters) - Growth in China's services sector accelerated in June, an official survey showed on Friday.

The official non-manufacturing Purchasing Managers' Index (PMI) rose to 53.7, compared to the previous month's reading of 53.1 and well above the 50-point mark that separates growth from contraction on a monthly basis.

Beijing has been counting on a strong services sector to pick up the slack as it tries to shift the economy away from a dependence on heavy industry and manufacturing exports.

(Reporting by Elias Glenn; Editing by Kim Coghill)