Additionally, a private survey showed China's services activity expanded at the fastest pace in three months in October.
The dollar was on the defensive and gold was little changed as the U.S. presidential election got underway, with polls predicting a tight race.
Oil prices were subdued in Asian trade after rallying almost 3 percent on Monday following OPEC+'s decision to delay restoring barrels to the market.
China's Shanghai Composite index jumped 2.32 percent to 3,386.99 and Hong Kong's Hang Seng index added 2.14 percent to close at 21,006.97 after Chinese Premier Li Qiang said he is confident of meeting this year's growth target and that there was room for more stimulus.
There was also some cheer on the data front. China's service activity expanded at the fastest pace since July, a private survey showed today in a sign that consumer demand may be on the mend.
The services sector in China continued to expand in October, and at a faster rate, the latest survey from Caixin revealed on Tuesday with a PMI score of 52.0.
That's up from 50.3, and it moves further above the boom-or-bust line that separates expansion from contraction.
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