The two children have been identified as 12-year-old Savita, a resident of Kaisarganj and five-year-old Seetesh Singh, a resident of Mahsi, District Magistrate Ajay Deep Singh said.
He said that Ghaghara river was flowing above danger mark at two places and flood water has entered a large number of schools in Mahsi and Kaisarganj tehsils.
Heavy rains in Nepal and terai regions and water released by the neighbouring country are said to be the cause of swelling of river Ghaghara in the district.
"Central paramilitary forces and NDRF have been pressed into action for rescue work and also to provide relief material to the flood-affected people. For the last three days, there has been a continuous rise in the water level of Ghaghara. This has affected 32 village panchayats in tehsils of Mahsi, Kaisarganj and Nanpara," the DM said.
So far, NDRF jawans have evacuated nearly 650 persons, he added.
To prevent spread of diseases, doctors and veterinary teams are being sent to the flood-affected areas, the DM said, adding that as many as 22 baadh chowkis (flood outposts) have also been established to facilitate relief work.