BERLIN, Jan 4(Reuters) - Business activity in the German services sector declined slightly in December, while price pressures rose, a survey showed on Tuesday.

The HCOB final services Purchasing Managers' Index (PMI) fell to 49.3 in December from 49.6 in November, pointing to a slightly faster contraction, although only slightly below the 50 level that signals growth in activity.

"The downward trajectory of service sector output persists for the third consecutive month, with no clear indications of an imminent turnaround," said Cyrus de la Rubia, chief economist at Hamburg Commercial Bank.

The manufacturing PMI remained below 50 throughout the fourth quarter, suggesting Germany is on track to register two consecutive quarters of declines in GDP and marking a technical recession, according to de la Rubia.

Labour market conditions weakened as services firms trimmed workforce numbers slowly in line with falling demand and amid sharply rising wages, the survey showed.

Average prices charged by services firms also rose more sharply in December, according to the report.

"In the service sector, inflation remains stubbornly high, defying the economic downturn," de la Rubia said. "Input prices are on a surprisingly rapid ascent."

Looking ahead, growth projections for the next 12 months in the service sector remained muted, with a combination of political and economic uncertainty reportedly weighing on expectations, the survey showed.

The composite PMI index, which comprises services and manufacturing, remained in contraction territory in December for a sixth straight month, falling to 47.4 from 47.8 in the previous month. (Reporting by Maria Martinez; Editing by Hugh Lawson)