HONG KONG, Oct 10 (Reuters) -

Chinese stocks declined on Tuesday as investors rushed to sell companies with exposure to the Middle East, while the Hong Kong market gained driven by dovish comments from U.S. Federal Reserve officials.

** China's blue-chip CSI 300 Index dropped 0.51%, while the Shanghai Composite Index fell 0.50%.

** Hong Kong's Hang Seng Index rose 1.29%, and the Hang Seng China Enterprises Index climbed 1.35%.

** Broader Asian shares rose on Tuesday in line with Wall Street's high note. Top Fed officials indicated on Monday that rising Treasury yields could mean less need for the policymakers to raise rates further.

** Mainland China investors, meanwhile, put more focus on the Middle East conflict after mixed Golden Week holiday consumption data.

** CSI Construction Engineering Index slumped 4.4%, led by a 9% tumble in state-owned China Communications Construction which signed contracts worth $3 billion in the Middle East in the past three years.

** China's belt and road-related stocks also fell 2%.

** Meanwhile, China said its Commerce Minister Wang Wentao and U.S. senators led by Senate Majority Leader Chuck Schumer held "rational and pragmatic" discussions on Monday.

** In Hong Kong, sentiment is marginally picking up due to the attractive valuation, analysts say.

** "As the focus turning to Q3 earnings, selling may have been exhausted somewhat and upside surprises in upcoming earnings may trigger a tradable rally," said Redmond Wong, Greater China market strategist at Saxo Markets.

** Hong Kong-listed tech giants jumped 1.6% by the midday break.

** Country Garden fell 3.6% after the embattled property developer said it might not be able to meet all of its offshore payment obligations when due or within the relevant grace periods. (Reporting by Summer Zhen; Editing by Varun H K)