NEW DELHI—Warships and aircraft from the U.S., India and Japan practiced hunting enemy submarines during wide-ranging exercises in the Bay of Bengal during the weekend, signaling the three powers’ deepening ties as they contend with a more assertive China.

Worries about Beijing’s rapidly increasing military strength and its growing ability to deploy forces far from Chinese shores have helped drive a convergence of strategic thinking in Washington, New Delhi and Tokyo and prompted pledges of defense and economic cooperation.

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