After a 15-minute delay in the start of the session, play continued for a little over one hour when foggy conditions forced a suspension.
Bangladesh were 59 for three in 17 overs in reply to India's first innings total of 243. The hosts trail the visiting side by 184 runs.
While Indian pace spearhead Zaheer Khan picked up two wickets, fellow pacer Ishant Sharma grabbed one.
Earlier in the morning, the start to the day's proceedings had been delayed by 90 minutes due to bad weather.
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