Punpun was flowing 2 cm above the danger level in Sripalpur, Kamlabalan in Jhanjharpur by 3 cm and Kosi in Baltara by 1 cm in Khagaria district, as per the information available with the Water Resources department.
Other rivers, including Ganga, were flowing below danger mark, it added.
The toll in Bihar floods, including earlier one in Kosi region triggered by heavy rains in terai region of Nepal, remains at 213.
The flood has affected 40.60 lakh people in 2,190 villages, the statement said.
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About 4.03 lakh people have been evacuated from the flood-hit Buxar, Bhojpur, Patna, Vaishali, Saran, Begusarai, Samastipur, Lakhisarai, Khagaria, Munger, Bhagalpur and Katihar districts, the statement said.
The government has deployed 2,973 boats for evacuation, while national and state disaster response forces have already been pressed into service in the affected districts.
A total of 257 relief camps are in function where 1.50 lakh people continue to take shelter.
The extent of damage to agricultural areas and crops loss was being estimated.