The boat sank close to Katha village, 20 km from the district headquarters.
Police and PAC personnel have fished out 22 bodies so far while 10 others have been rescued, he said. A search was on to trace others.
"The boat was ferrying passengers more than its capacity. Most of the passengers of the ill-fated boat were women. As soon as the boat reached mid-stream it capsized," the district magistrate said.
Uttar Pradesh Chief Minister Yogi Adityanath expressed grief over the incident.
In a tweet, he issued instructions that the kin of the deceased be given Rs 2 lakh as relief from the chief minister's relief fund.
The chief minister also directed the district magistrate to immediately provide succour to the affected people, Principal Secretary (Information) Awanish Awasthi said.
He said a probe has been ordered into the incident.
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