Germany's manufacturing sector, which accounts for about a fifth of its economy remained mired in a downturn in August on weak demand and rapidly falling output, a survey showed on Friday.

The HCOB final Purchasing Managers' Index (PMI) for manufacturing rose to 39.1 in August from 38.8 the month before, in line with a flash estimate and still far below the 50 level separating growth from contraction.

The small rise was due to a quickening of lead times on purchases for the 10th month in a row, the survey showed, helped by lower input demand that freed up capacity and improved material availability.

However, August's reading was still the second-lowest since May 2020 and the 14th in a row below 50.

The fall reflects a quickening drop in output, which fell to its lowest reading since May 2020, while customer uncertainty, an ongoing destocking cycle and a general lack of appetite for investments led to rapidly declining new orders.

Cyrus de la Rubia, Hamburg Commercial Bank chief economist, said a slowdown in the pace of destocking and the stabilization of deteriorating new orders pointed to the sector starting to bottom out, though that would take time.

"The darkest hour is just before dawn. This may be the situation the German manufacturing sector is in," he said.

"...We are confident that the destocking cycle will come to an end during the fourth quarter and that should set a good tone for 2024." (Reporting by Miranda Murray; editing by John Stonestreet)