A toddler and a nine-month old died after their home in Faridabad town was set on fire early on Tuesday, allegedly by upper-caste men.
Three people were arrested and police said they were looking for nine others.
The parents of the children were also injured and their mother is reported to be still in a critical condition.
Security has been tightened in the area after a rise in tensions over the incident.
On Tuesday, several young men blocked roads in Faridabad, demanding action against those behind the crime. Many more joined them on Wednesday, local television reported.
The chief minister and senior police officials have promised to bring the attackers to justice.
The attack appeared to have been part of a long-running feud between the area's Dalit community and the higher Rajput caste, which also claimed the lives of three people a year ago.
Dalits, formerly known as "untouchables", are at the bottom of the Hindu caste system in India. Although caste discrimination is illegal, biases remain in many areas.