* 31.8 pct see Q4 prices rising, from 31.2 pct in survey for Q3
* Q4 price falls expected by 10.3 pct of households
* Fewer now feel monetary policy is relatively tight (Adds details, c.bank survey on monetary policy)
BEIJING, Sept 15 (Reuters) - The percentage of Chinese households that believe still-hot housing prices will keep rising in the coming quarter, despite state moves to cool them, remains at nearly one-third, a survey by China's central bank showed on Friday.
The People's Bank of China said its survey of 20,000 households found that 31.8 percent predicted a price rise in the fourth quarter.
That was slightly above the 31.2 percent who felt that way in the survey for the third quarter.
China's property prices have continued to creep steadily higher, in spite of heavy government intervention, partly due to a shift to increased demand in the country's smaller cities.
Prices of new homes in 70 major cities grew 9.7 percent in July from a year ago, with a monthly increase of 0.4 percent, official data showed.
The latest survey results highlights the challenges Chinese policymakers face as they tread carefully to tame a property market without bursting the bubble and dealing a blow to economic growth.
China's real estate investment and sales growth picked up pace again in August as demand held up.
In the latest central bank house-price survey, 10.3 percent of households predicted a price fall in the coming quarter, compared with 9.6 percent three months ago.
The percentage predicting that house prices would be "basically unchanged" in the next quarter was 46.1 percent - identical with the number from the survey about third-quarter expectations.
Beijing has tightened monetary conditions this year to tackle its growing debt pile as mortgages soar, but credit is still growing faster than economic output and most China watchers don't expect the central bank to tap too hard on the brakes.
A separate central bank survey published on Friday showed Chinese bankers who believe China's monetary policy is "relatively tight" in the third quarter fell to 22.1 percent, down 8 percentage points from the second quarter. (Reporting by Beijing Monitoring Desk and Yawen Chen; Editing by Richard Borsuk)