"My government has already completed its R&R in 2008 corresponding to full dam height of 138 meters," he said in a tweet.
Chouhan said the present permission is to install gates in open position and as such does not result in any increase in present level of submergence.
He said the permission to impound water at higher levels by NCA is after construction and after satisfying that submergence area is completely vacated.
In a statement, Singh said he would like to know if this decision had been taken in concurrence with Chouhan's will.
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He said the Union Environment Ministry which monitors such projects should also state if people who would be affected due to increase in dam height have been rehabilitated or not.
Sardar Sarovar Project is an on-going inter-state multipurpose project on river Narmada and is being constructed by Gujarat. The project envisages hydro-power generation of 1450 MW to be shared by Madhya Pradesh, Maharashtra and Gujarat.
The project would also supply drinking water to 135 urban centres and 8215 villages in Gujarat and two urban centres and 1107 villages in Rajasthan.
The foundation stone of the dam was laid by country's first Prime Minister Jawaharlal Nehru on April 5, 1961. The project, however, got embroiled in controversy over issues of displacement of thousands of project-affected people.
However, the Supreme Court had earlier given the approval for the project to raise the height of the dam to 138.72 metres.