The man who had held the children hostage was killed, Additional Chief Secretary Avanish Awasthi told PTI.
Earlier, a team of NSG (National Security Guard) commandos has taken a special aircraft to reach Farukhabad, a senior security official in Delhi said.
Police said Batham handed over the girl to his neighbour from a balcony.
The motive of the accused was not known immediately.
Chief Minister Yogi Adityanath monitored the situation in Farrukhabad, which is nearly 200 km from state capital Lucknow.
Television channels have appealed to Batham to contact them in case he wanted to share his demands with the government or authorities.
"We are ensuring the safe rescue of the children and if needed, the NSG will also be called for the operation," the DGP said earlier.
He said that commando units have been directed to reach the village.
Police said Batham is a murder accused and he seems to be mentally unstable.
"Twenty children are being held hostage at Kasaria village," Additional Director General of Police P V Rama Shastri said.
Inspector General of Police, Kanpur Range, Mohit Agarwal, said, "The man called the children for a birthday party and held them hostage in the basement of the house. He fired six shots from inside the building."
He said Batham, who appears to be mentally unstable, fired on those who attempted to speak to him.
Batham wanted to talk to the local MLA, but he refused to speak to the leader when he arrived, Agarwal said.
The chief minister is personally monitoring the situation and has directed top officials to ensure the immediate release of the children without any physical harm, officials said.
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