Share markets in the mainland extended the previous day's gains amid news that the government may be stepping up on fiscal policy to support the economy; the benchmark Shanghai Composite index closed up 2.32 percent.  Market watchers say state-backed buying, which helped to underpin a late-day swing in the mainland markets on Tuesday, also restored battered investor confidence.  "Usually when we see these [swift] rallies in financial and energy stocks, most of the time it's by the Chinese government. They do that to make the index look good and restore investors confidence," Jackson Wong, associate director at United Simsen Securities Limited, told CNBC. "[Today] the rally has continued because investors are more confident."  Among China's other indexes, the blue-chip CSI300 Index and the smaller Shenzhen Composite advanced 2 and 3.3 percent, respectively.  Hong Kong's Hang Seng index jumped 4.1 percent to its highest level since August 28, with Cheung Kong Infrastructure Holdings up 4.3 percent following news that the infrastructure arm of Li Ka-shing's conglomerate is planning to buy the rest of Power Assets Holdings it doesn't already own. Shares of Power Assets went up 6 percent.  Meanwhile, the China Enterprises Index, which tracks Chinese companies listed in Hong Kong, leaped 5.2 percent.  Read MoreChina's latest step to curb stocks' wild ride: Circuit breakers  According to a statement by the Ministry of Finance late Tuesday, China will accelerate major construction projects, bring in private financing through increased use of the public private partnership (PPP) model, standardize the management of local government debt and reform taxes.  Meanwhile, the National Development and Reform Commission (NDRC) approved two railway projects on Tuesday with a total value of nearly 70 billion yuan ($11 billion), the latest move to support infrastructure projects to re-energize sputtering growth.  Authorities also said late Monday it would remove personal income tax on dividends for shareholders who hold stocks for more than a year. According to Bert Hofman, country director for China, Mongolia and Korea at The World Bank, this move encourages longer-term investment in equities which will likely pave the way for more stability in the market.
Asian shares were on a roll Wednesday, as investor confidence got a boost from the strong rally in offshore markets.