Business activity in China's service sector expanded at its slowest pace in two and a half years in January, a private survey showed on Friday.

The HSBC/Markit China services purchasing managers' index (PMI) posted at 50.7 in January, continuing the fall from 50.9 in December and 52.5 in November, adding to concerns about a moderation in the world's second-largest economy.

PMI above 50 percent indicates expansion; below 50 percent, contraction.

Despite weakening business conditions at the start of the year, Chinese service providers were optimistic in January, generally expecting activity levels to be higher than current levels over the next year. Optimism was largely driven by forecasts of improving economic conditions and new product launches.

Qu Hongbin, HSBC's chief China economist, said the slower expansion reflected soft manufacturing growth and the impact of government measures to curb extravagance.

"As business sentiment remains stable, we expect service growth to bounce back a little in the coming months," Qu said, adding that a meaningful improvement relies on stronger manufacturing growth and service sector reform.

The National Bureau of Statistics and the China Federation of Logistics and Purchasing on Monday released the official PMI for the non-manufacturing sector in January, which also fell to the lowest since February 2012: 53.4.

Both official and HSBC manufacturing PMI showed a slowing in January.

Annual economic growth slowed to 7.7 percent in the fourth quarter of 2013 from the third quarter's 7.8 percent, settling full-year growth at 7.7 percent, slightly above the government 7.5 percent target.

Although headline GDP growth remains stable, analysts expect further moderation as authorities turn their attention to a more sustainable model and various reforms.