BERLIN (Reuters) - Rising output and order levels helped German manufacturing expand faster in October, a survey showed on Monday, in a sign the sector is increasingly helping underpin growth in Europe's largest economy.

Markit's Purchasing Managers' Index (PMI) for the German manufacturing sector, which accounts for around one-fifth of the economy, rose to 51.7 from 51.1 in September.

The reading was higher than a preliminary estimate of 51.5 and above the 50 mark separating growth from contraction for the fourth consecutive month, signalling a sustained recovery in the manufacturing sector.

"Manufacturing business conditions improved again in October, with production volumes rising at a solid clip and new orders expanding at one of the fastest rates seen over the past two-and-a-half years," said Tim Moore, an economist at Markit.

"Increased export sales contributed to the upturn in new order inflows, with robust growth in the investment goods sector helping offset weakness in consumer goods."

The German economy put in a strong performance during the early years of the euro zone crisis but weakened last year and suffered a subdued start to 2013.

While it bounced back in the second quarter, economists generally expect slower albeit solid growth for the remainder of this year.

The PMI survey showed factories taking in more orders from abroad for the third month running, although the rise was less marked than in September. A timid recovery across Europe is lifting German exports, which have languished this year.

Manufacturing firms cut jobs at a slightly faster pace than in the previous month but a rise in backlogs of work suggested that they could start hiring more in the months ahead.

Their costs rose, albeit marginally, for the first time since November 2012. But they compensated for this by raising their output prices.

(Reporting By Sarah Marsh; Editing by Hugh Lawson)