BERLIN (Reuters) - Weaker growth in services prompted a very slight drop in German private sector activity in June, a survey showed on Tuesday, but confidence about future workloads added to hopes that the economy will continue expanding.

Markit's final composite Purchasing Managers' Index (PMI), tracking activity in manufacturing and services that together account for more than two-thirds of the economy, fell to 54.4 from 54.5 in May.

The reading was higher than a preliminary estimate of 54.1 and comfortably above the 50 mark that separates expansion from contraction.

"Today's PMI numbers signal a note of caution for German service providers, with activity and new orders both rising at the weakest rates in roughly a year," said Markit economist Oliver Kolodseike.

He added that the transport and storage services sub-sector acted as a major drag on stronger growth.

The German economy grew 0.7 percent in the first quarter, more than doubling its growth rate and cementing its role as the euro zone's growth engine. Soaring private consumption and a construction boom more than offset a dip in foreign trade.

The government expects GDP to expand by 1.7 percent this year, on a par with last year.

"Confidence also remained at a historically high level, adding to hopes that economic growth will continue into the second half of the year," added Kolodseike.

The PMI sub-index for services fell to a 13-month low of 53.7 in June from 55.2 in May. Services providers continued to hire staff, making the rate of job creation the strongest so far this year.

The sub-index for manufacturing, which was published on Friday, showed rising domestic and foreign demand lifted German factory activity to a 28-month high in June.

((Reporting by Joseph Nasr; Editing by Hugh Lawson))