BEIJING, Jan 12 (Reuters) - China's consumer prices extended their decline for a third month in December while factory-gate prices also fell, highlighting persistent deflationary pressures in an economy struggling to mount a solid recovery.

The consumer price index (CPI) shed 0.3% in December from a year earlier, and was up 0.1% month-on-month, data from the National Bureau of Statistics (NBS) showed on Friday. November's index dropped 0.5% in annual and monthly terms.

Economists polled by Reuters forecast a 0.4% fall in consumer prices year-on-year and a 0.2% gain month-on-month.

The producer price index (PPI) slid 2.7% after a 3% fall in November, marking the 15th straight month of declines. Analysts had expected a 2.6% tumble in December.

With a protracted housing downturn, a soft job market and other headwinds such as debt risks dampening growth prospects, consumers in the world's second largest economy have been tightening the purse strings.

(Reporting by Qiaoyi Li, Liangping Gao and Ryan Woo Editing by Shri Navaratnam)