Some 10,000 of Madhepura's 45,000 residents fled soon after Kosi began shifting from its course on August 18.
More than 800 people have died in flooding and the government has sent in the army to help relief efforts in Bihar state, where whole villages are under water.
"A couple of days ago just a handful of districts were affected and today there are 15 which are under water," Mukesh Kumar told an AFP news agency correspondent in Madhepura, some 225km from the state capital Patna.
"We need a massive rescue effort," said local council member Kumar.
Among those hit was Shanti Devi, who dragged her two children out of their house as the waters rose.
"The government is asking us to escape but we have nowhere to go," the 32-year-old mother said.
Nitish Kumar, the Bihar chief minister, advised panic-stricken people to "run" in an overnight address on state-run radio.
"Time is running out for these luckless people," Narendra Narayan Yadav, the state revenue minister in Madehpura where the swirling water has overrun train tracks and the main highway, warned.
People were using rowboats or a few backroads still above the rising water levels to flee.
The force of the water was washing away about 150 metres of the Kosi's protective levee every day, Nitish Mishra, Bihar's disaster management minister, said.