The China Enterprises Index of Hong Kong-listed mainland companies , or H shares, eased 0.19 percent.
Shanghai stocks dropped 1.38 percent as investors were disapointed at weak regulatory steps to curb the sale of listed shares.
STOCKS ON THE MOVE:
Fubon Bank surged 9.11 percent on Tuesday on optimism that the Taiwanese bank will benefit from investing in China.
Taiwan's regulator said earlier this month it approved Fubon Financial's 2881.HK plan to buy a stake in Xiamen City Commercial Bank via Fubon Bank (HK) Ltd.
The stock has risen nearly 50 percent since April 14.
Oil refiners continued to rise after Beijing said on Sunday it would provide a subsidy against losses due to refining imported crude oil.
Shares in top Asian oil refiner Sinopec Corp jumped 2.41 percent on Tuesday and PetroChina Co Ltd. Asia's largest oil and gas producer, also rose 1.78 percent.
Shares of China Mobile, the world's largest telecoms carrier, fell 2.0 percent after it reported a 37 percent rise in quarterly net profit, slightly shy of forecasts.
The net was driven by strong subscriber growth although average revenue per user slid as the world's top cellular carrier signs on more low-end subscribers.




