In a statement, the Indian Ministry of Electronics and IT said many innocent people had been lynched as a result of these messages circulating on WhatsApp.
It said while the country's law enforcement authorities were taking steps to apprehend those responsible for such acts, "the abuse of platforms like WhatsApp for repeated circulation of such provocative content is equally a matter of deep concern".
WhatsApp, which is owned by Facebook, has said that it is "horrified" by the "terrible acts of violence".
Five people were lynched in Maharashtra's Dhule district earlier this month, after rumours were spread on WhatsApp that they were child abductors. Twenty-three people have been arrested in connection with the killings.
Further, a man was detained for circulating his cousin's photo on WhatsApp and branding him as a child abductor.
The government statement said: "It has also been pointed out that such platforms cannot evade accountability and responsibility, specially when good technological inventions are abused by some miscreants who resort to provocative messages which lead to spread of violence.
"The government has also conveyed in no uncertain terms that WhatsApp must take immediate action to end this menace and ensure that their platform is not used for such malafide activities."
India is the country with the widest use of WhatsApp and about 90% of the smartphones in use have the application installed. Indians spend 50 million minues a day making video calls on WhatsApp, making it by far the highest usage of this function.