BEIJING, Oct 1(Reuters) - New home prices in China fell for the third straight month in September as a mortgage boycott across the country and a slowing economy discouraged potential home buyers, a private survey showed on Saturday.

China's property market crisis worsened this summer, with official data showing home prices, sales and investment all falling in August, adding pressure on the world's second-largest economy, which barely grew in the second quarter.

Prices in 100 cities fell 0.02% in September from a month earlier, after declines of 0.01% in July and August, respectively, according to a survey by China Index Academy (CIA), one of the country's largest independent real estate research firms.

Among the 100 cities, 56 cities posted a fall in monthly prices, compared with 69 in August, the survey showed.

Official new home prices for September will be released by the National Bureau of Statistics on Oct. 19.

The chill in the sector deepened after a number of overleveraged leading developers defaulted on bonds and failed to complete projects or even start new ones, prompting many homebuyers to stop repaying mortgages and keeping a lid on demand for new homes.

Sporadic COVID-19 lockdowns have also dampened consumer confidence, while job losses and weak economic growth have made many more careful about their spending.

To prop up the distressed sector, many small cities have taken steps this year such as reducing down-payments, cutting mortgage interest rates, and offering better terms for households with more than one child.

Local governments will now be able to relax the floor on mortgage rates for first-time home buyers in some cities in phases, the central bank said on Thursday.

In the fourth quarter, local governments can be expected to further implement measures to shore up their respective markets while continuing to guard against speculative purchases, said Cao Jingjing, a CIA analyst. (Reporting by Liangping Gao and Ryan Woo; Editing by Kim Coghill)