NEW DELHI—India retaliated for the arrest of one of its diplomats in New York by dismantling security barriers on streets around the U.S. Embassy in New Delhi and revoking some privileges given to American consular officials.

U.S. prosecutors last week charged Devyani Khobragade, an Indian consular officer in New York, with committing visa fraud and making false claims about the amount of money she paid an Indian national who worked for her as a domestic helper.

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