BERLIN (Reuters) - Growing new business helped Germany's private sector expand at the fastest pace in seven months in August, a survey showed on Wednesday, suggesting Europe's largest economy will post robust growth this quarter.

Markit's final composite Purchasing Managers' Index (PMI), measuring growth in both the manufacturing and services sector and covering more than two-thirds of the economy, rose to 53.5 in August from 52.1 the previous month.

The index stayed above the 50 line that separates growth from contraction for the fourth month running and was marginally above an initial reading of 53.4.

Signs of a pickup in Europe's largest economy will be welcome for conservative Chancellor Angela Merkel, who is courting votes before Germany's September 22 federal elections.

"Germany's service economy joined its manufacturing sector in achieving an accelerated pace of output expansion in August, helped by the fastest rise in new business since the start of the year," said Tim Moore at Markit.

"August's data indicated that the combined output of Germany's manufacturing and service sectors rose at the sharpest pace for seven months, suggesting that the wider economy is well on track to continue expanding at a solid clip in the third quarter of 2013."

A bastion of strength in the early stages of the euro zone's debt crisis, the German economy only narrowly avoided recession at the start of the year as a worsening global outlook diminished appetite for its products and willingness to invest.

But the economy grew at its strongest rate in more than a year in the second quarter. Recent data has added further evidence that it is bouncing back from its brief slowdown.

Business sentiment hit its highest level in 16 months in August and consumer sentiment remained close to its highest level in nearly six years, surveys showed last week.

A separate Markit survey released earlier this week showed manufacturing grew at the fastest pace in two years in August thanks to robust demand at home and abroad.

Wednesday's survey showed the PMI tracking the services sector edging up to 52.8 in August from 51.3 the previous month. The final reading came in above a flash estimate of 52.4.

New business in the services sector expanded for the second month in a row, while backlogs of work grew for the first time since February last year, the survey showed. Firms hired more staff for the second month running.

"Another increase in services employment highlighted that companies are increasingly confident about the business outlook for the months ahead," said Markit's Moore.

(Reporting By Sarah Marsh; Editing by Hugh Lawson)