BEIJING, Jan 1 (Reuters) - Chinese property prices rose again in December, according to two private surveys, but are showing signs of stabilising following government measures aimed at cooling the housing market and averting the threat of a bubble.

Prices of new homes in 288 cities in December rose 0.37 percent in December from November, when they had risen 0.77 percent, a poll by real estate services firm E-House China showed on Wednesday.

House prices climbed 10.04 percent from a year earlier, little changed from November's annual rise of 10.11 percent and a seventh consecutive month of double-digit annual gains.

A separate survey by China Real Estate Index System (CREIS) on Tuesday showed average prices in the 100 biggest cities rose 0.7 percent in December from November, when they had risen 0.68 percent, to post a 19th straight monthly gain.

On average, prices rose 11.5 percent in December from a year earlier, CREIS said in a statement, with prices in seven cities including Beijing and Xiamen increasing by 20 to 30 percent.

"With the housing supply increasing in 2014, shortages are likely to be eased and developers will become more rational," said CREIS, a consultancy linked to China's largest online property information firm, Soufun Holdings.

"But there might be increasing divergence between big and small cities," it added.

House prices have surged in the past year, in part due to a view that property remains one of the best investments. That has prompted the government to try to head off bubbles in the market without damaging one of the pillars of growth in a slowing economy.

Despite the steps, which include clampdowns on mortgage lending, increased construction of affordable homes and promises of more land for building, many Chinese find home ownership well beyond their reach.

Analysts say Beijing won't want to see a sudden and sharp downturn in the property market as the leadership tries to steer the world's second-largest economy towards more sustainable growth after three decades of breakneck expansion.

The economy is expected to have grown about 7.5 percent in 2013, the weakest pace since the Asia financial crisis in the late 1990s.

A Reuters poll in November had predicted a slowdown in house price growth, with analysts forecasting a 5.0 percent rise in house prices in 2014 after a 10 percent gain last year.

Official data for 70 cities for November released last month showed prices rose 0.5 percent in November in month-on-month terms, the third straight slowdown.