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The tremor was recorded at 12.12 am with its epicentre 22 km east-south east of Khavda, the Gandhinagar-based institute said in its latest update.
District authorities said no casualty or damage to property was reported.
Kutch district is located in a very high risk seismic zone, where earthquakes of lower intensity occur regularly.
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The district recorded a tremor of 3.2 magnitude on March 5 and of 3.5 intensity on March 11, as per the ISR record.
The 2001 earthquake in Kutch was the third largest and second most destructive in India over the last two centuries. Around 13,800 persons were killed and 1.67 lakh injured, while a large number of towns and villages in the district suffered almost complete destruction.