The government warned the company in June that it was its last chance to comply with blocking orders, according to sources.
India's information technology law allows the government to block online content that endangers the security of the state.
They said that because of the seriousness of the threats, they decided to go to court.
Sources said that the social media giant believes that many of the orders are disproportionate and that they are deficient.
The sources said that there are demands for entire accounts to be blocked. There are several accounts that involve content posted by political parties.
This is the latest in a series of confrontations between the government and the social networking site.
Over the past year, authorities have asked the social media giant to take down accounts due to public order concerns. Last year's massive protests by farmers and the government's handling of the epidemic are included in these accounts.
In response to a legal notice by the government, some 250 accounts were temporarily blocked by the social networking site.
There were accounts of an investigative news magazine and activists who supported the protests on the outskirts of Delhi.
It took six hours for the accounts to be restored.
In February of last year, it was told that it was welcome to do business in India, but it had to follow the laws of the country.
The freedom of expression in India was brought to the attention of the social networking site in May.
The site was served a notice by the police after it was accused of being manipulated.