Her body was found on Sunday close to her home from where she was allegedly abducted on the night of 8 December.
The extent of the injuries to the child have horrified Indians, with many drawing parallels with the 2012 Delhi bus rape that caused massive outrage.
The child’s mother told that they wanted justice.
“It’s been 24 hours and the police are yet to catch anyone,” she said.
Police have detained three of her husband’s relatives for questioning but no arrests have been made so far. However no details have been released.
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The government has formed a special investigative team as public pressure mounts on authorities to catch those responsible for the crime. Locals, including activists and political leaders from the district, have gathered in the village to protest.
The girl’s family is demanding an inquiry by the federal police, saying they have no faith in the local police.
The girl’s father, a rag picker, said he was away on work the night his daughter was abducted.
When his wife woke up the next morning, he said, she realised one of their daughters was missing. The couple have three other children – two sons and one daughter.
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The family lives on a plot of land along with four other families in a Haryana town. Police suspect those who raped and killed the girl could have come from a nearby slum.
The girl’s family had initially refused to cremate her until the killers were caught. The funeral only went ahead after the police assured them that they would make an arrest soon.
They have set a deadline for the police – 11am on Wednesday morning – to make an arrest. If that doesn’t happen, they have threatened to escalate the protest.
In another incident, one man has been arrested over the alleged gangrape of a teenage cancer patient from the northern state of Uttar Pradesh.
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The girl has alleged that she was abducted and raped by two men, and when she approached a neighbour for help he raped her as well.
Scrutiny of sexual violence has grown in India since the 2012 gang rape and murder of a 23-year-old student on a bus in the capital Delhi.
The crime sparked days of protests and forced the government to introduce tougher anti-rape laws, including the death penalty.
However, brutal sexual attacks against women and children continue to be reported across the country.