Shares pushed to new highs soon after the open of trade on Tuesday following another rally on Wall Street as lawmakers agreed a budget deal to reopen the US government.

The Hang Seng Index rose 0.66 percent, or 212.73 points, to 32,606.14.

And the benchmark Shanghai Composite Index inched up 0.09 percent, or 2.98 points, to 3,504.34 but the Shenzhen Composite Index, which tracks stocks on China's second exchange, was flat, dipping 0.55 points to 1,943.36.

Shares surged more than one percent in Hong Kong on Tuesday, ending the morning at fresh records, as global traders press on with a rally fueled by optimism about corporate earnings.

The Hang Seng Index jumped 1.18 percent, or 382.47 points to 32,775.88 by the break.