ROME, July 3 (Reuters) - Italy's services sector expanded for a sixth month running in June albeit at a slower pace than the month before, a survey showed on Wednesday, amid sustained growth in new business in the euro zone's third-largest economy.

The HCOB Purchasing Managers' Index (PMI) for Italian services came in at 53.7 in June, down from 54.2 in May but still comfortably above the 50 level that separates growth from contraction.

"Despite a slight decline from the previous month, the Services Business Activity Index remains robust," said HCOB economist Tariq Kamal Chaudhry.

The reading matched the median forecast in a Reuters survey of seven analysts.

The PMI survey's new business sub-index stood at 53.0, slightly down from 53.3 in May, while the employment indicator declined to 53.1 from 54.1, both remaining well above the key 50 mark.

In contrast to service providers, the PMI for Italy's smaller manufacturing sector, released on Monday, pointed to contraction for a third month running in June.

The composite Purchasing Managers' Index, combining services and manufacturing, declined to 51.3 from May's 52.3, posting the lowest reading since February but remaining above the 50 threshold for a sixth consecutive month.

Italian economic growth probably weakened in the second quarter, the country's budget watchdog said last month, after gross domestic product expanded by 0.3% between January and March.

Most analysts forecast modest full year growth of between 0.7% and 1%, broadly in line with last year's 0.9% rate. (Reporting by Angelo Amante; editing by Gavin Jones and Christina Fincher)