He also announced Rs 2 lakh each for the next of kin of those who have lost their lives due to floods in Arunachal Pradesh, Manipur, Mizoram, Nagaland and Tripura, the Prime Minister's Office (PMO) said.
The seriously injured people will get Rs 50,000 each, the PMO said.
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"The prime minister had released Rs 300 crore in June. The Rs 250 crore announced today was in addition to the amount released in June," he said.
"The problem in the north east is India's problem and we should collectively concentrate on converting the problem in to power," Water Resources Minister Keshab Mahanta quoted the prime minister as saying.
Modi, during his day-long visit here, met chief ministers of Assam, Arunachal Pradesh, Manipur and Nagaland to take stock of the situation arising out of the floods.
Mizoram Chief Minister Lal Thanhawla did not come but sent a representation on his behalf.
"The prime minister announced Rs 2,350 crore total flood package for the north eastern states,"Sarma told reporters here.
Giving a breakup, Sarma said, "The prime minister has announced a special package of Rs 2,000 crore for all the north eastern states for relief and rehabilitation of flood damage."
The exact share of different states will be worked out in coming days and will be announced accordingly, he added.
In addition to that, the prime minister announced a Rs 100 crore corpus for setting up a research project to study Brahmaputra river and its role in creating devastating flood, Sarma said.
The package will be for flood relief, rehabilitation, reconstruction measures for affected states of the northeast, the prime minister said later.
"The package will have a significant component devoted to infrastructure & improving water holding capacity of the Brahmaputra," he tweeted.
"We are exploring all possible means to enable proper management of the water resources of the northeast. This will help us immensely," Modi added.
Sarma said the research project to study Brahmaputra will have a high-power committee comprising scientists, researchers, engineers.
"They will study the river and suggest remedies to tackle floods. This will be long term project," the finance minister of Assam added.
The prime minister said the Centre is always with Assam and the north eastern states and suggested adoption of short and long term measures to handle flood and erosion problems.
Assam Chief Minister Sarbananda Sonowal presented Rs 3,888.09 crore loss due to the latest wave of flood in the state to Modi.
The Assam government, however, did not submit any memorandum but sought support in rebuilding infrastructure and other rehabilitation works, Mahanta said.
Nagaland Chief Minister T R Zeliang sought at least Rs 700 crore for damages caused by latest wave of floods but declined to say whether the prime minister had assured him of funds.
"We have assessed our damage and it is Rs 700 crore. So for rebuilding the infrastructure and other purposes, we need assistance beyond Rs 700 crore," Zeliang told reporters after meeting PM Modi here.
During this year's flood in Nagaland, 18 people have lost their lives. Around six lakh people were affected and 6,000 villages were hit, he said.
"It was a big natural calamity this time. There were heavy floods and landslides at many places. The hardship of people still continues.
"It is good and encouraging that the Prime Minister has come and met all the CMs of the north east. This is a good sign," Zeliang said.
Modi also promised help and support to Arunachal Pradesh Chief Minister Pema Khandu, who submitted a memorandum to him on the damages caused by the floods, in providing relief, rehabilitation and rebuilding infrastructure in the flood-affected hill state.
"The prime minister gave a patient hearing to our problems and promised help and support in relief, rehabilitation and rebuilding the infrastructure," Khandu said after the meeting.
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