The petition filed by Anupam Bajpai, national coordinator of Jeevan Bachao Andolan, through advocate Shiv Kumar Tripathi is expected to be heard next week.
"If the population of India continues to multiply with the existing rate, the impact on the environment could be devastative," the petition read.
The petition, while suggesting that the number of children in each family be restricted to two, has proposed that the Centre link various welfare measures to people only if they comply with the two-child policy.
According to the petitioner, since India is the second-most populated country after China, there is a serious pressure on natural resources such as water, air and food grains.
The petitioner has cited the instance of China succeeding in reducing its population by adopting the one-child norm.
"It was able to reduce the population growth by about 300 million over 20 years. The various methods that were adopted to implement the one-child norm included IUDs, sterilisation and abortions as forms of birth control," the plea said.