Local governments in China announced a flurry of property market cooling measures over the weekend, seeking to douse fears about a real estate bubble.

Several cities tightened rules for home purchases, starting with capital city Beijing on Friday, which increased the down payment required on real estate purchases.

First-time buyers must now have a downpayment equivalent to 35 percent of the purchase price, up from 30 percent, while buyers of a second property will have to put down at least half of the selling price.

Residents of the inland city of Zhengzhou who already own two properties, as well non-residents who own one in the city, will now only be able to buy homes larger than 180 square meters, according to a notice posted on the local government's website late on Saturday.

The moves come after China's richest man, Wang Jianlin, told CNN that the country's property sector was in the "biggest bubble in history," noting that it was difficult for Beijing to avoid fanning overheated markets in some cities while stimulating broader economic growth.

"I don't see a good solution to this problem," he said. "The government has come up with all sorts of measures - limiting purchase or credit - but none have worked."

In Chengdu, the capital of southwest Sichuan province, which is renowned for its panda breeding program , prospective buyers will be allowed to purchase just one property in certain city districts, while those buying a second property will need to place a down payment of no less than 40 percent of the purchase price, the local government said.

The tier 2 eastern city of Jinan said on Sunday that residents who already owned three properties could not buy more; it also increased down payment requirements for those buying their first home to 30 percent from 20 percent, among other measures detailed in a document on the government's website.

Meanwhile, the neighboring city of Tianjin said it would stop people who do not have the local residence permit from buying a second property in the city's downtown area.

Wuhan, Hefei, Zhangzhou and Suzhou have also recently launched cooling measures, according to a Reuters report.

The measures come ahead of Chinese national holidays this week, and a week after data showed that average new home prices in China's 70 major cities rose 9.2 percent in August from a year earlier, accelerating from a 7.9 percent increase in July.

The official survey from the National Bureau of Statistics also showed that new home prices rose 1.5 percent in August from July. Some cities, however, showed signs of overheating.