The police report said the girls killed themselves "out of shame" after one of the sisters was seen with a boy.
But the girls' parents had accused the Central Bureau of Investigation (CBI) of "trying to fudge the case".
Rights groups and their relatives said many questions remained unanswered.
The lower-caste cousins, thought to have been 14 and 15, were found hanged from a mango tree on 28 May 2014 in Uttar Pradesh.
The initial reports that the girls had been gang-raped and murdered by a group of men from the same village sparked global outrage.
A local post-mortem examination initially confirmed multiple sexual assaults and death due to hanging.
But in December, the CBI filed a "closure report" in court, saying investigators had studied "around 40 scientific reports" and "questioned over 200 people" and come to the conclusion that the elder girl had "an intimate relationship" with one of the three men and that the other girl, her younger cousin, was "facilitating the relationship".
The girls killed themselves after they were found by a neighbour and because they were afraid of facing their families, the report added.
It accused the families of filing a false complaint of rape and murder and requested that the case be closed.
The girls' relatives accused the CBI of conducting "a shoddy investigation" and filed a "protest petition" in a local court in Badaun town.
On Wednesday, the special court that deals with cases of sexual offences against children rejected the CBI report and also summoned the main suspects in the case to the next date of hearing.
A CBI spokesman said they were yet to get the detailed court order and would comment only after studying it, the Indian Express newspaper reported.
Three men arrested in connection with the case and two policemen accused of "dereliction of duty" were freed on bail in September.

Marian Fields had an aggressive and very rare form of skin cancer, which left her with large, open wounds around her backbone following multiple operations and radiation treatments.
She was beginning to lose all hope of recovery after plastic surgeons in the US refused to take on her case because of the size of the wound.
But her identical twin sister Mary Jane provided the solution.
"There was never a moment of hesitation when the option to donate skin and tissue was a possibility," Mary Jane said.
"I had what she needed. We are two bodies with one soul. She is my other self."
Dr Jesse Selber, a plastic surgeon from the MD Anderson Cancer Centre at the University of Texas, who had previously performed the first skull-scalp transplant, said the surgery was "incredibly challenging and complex".
His team of five plastic surgeons removed skin, tissue and blood vessels from Mary Jane's abdomen and transplanted it to Marian's back, connecting eight different arteries and veins under a microscope during surgery.
The hole in Marian's back was 21.5in by 8.5in (55cm x 22 cm), making it one of the largest tissue transplantations on record.
By donating skin to her sister, Mary Jane - in effect - got a giant tummy tuck.
Having an identical twin made the transplantation process more likely to succeed for Marian because no suppression of her immune system was required - but there were still huge risks.
Surgeons said they were concerned about the donated skin being rejected and the possibility of the cancer recurring.
Although the tumour in Marian's back was very aggressive, it was not a type that spreads to other parts of the body so receiving her sister's skin and tissue was a perfect fix.
Dr Selber said: "Marian's wound was impossibly large - without her genetically identical sister, we would not have had enough tissue to reconstruct it."
The surgery took 14 hours and involved "extensive resection through skin, muscle and bone", followed by "hours of meticulous microvascular work".
This involved re-connecting countless veins and arteries.
The surgery was meticulously planned beforehand - and it paid off, according to Dr Selber.
"It went quite beautifully," he said.
Before the transplant surgery, Marian was in horrible pain. She couldn't lie on her back or sit up in a chair properly.
One month on from the surgery, the twins have been discharged, the stitches have been removed and they have returned home.
Marian says: "I'm looking forward to getting back to work, driving, running and sitting comfortably.
"I've never been sick before 2012 and am ready to get back to life."
An Indian court has rejected a federal police report which had ruled that two teenage girls found hanging from a tree in India last year took their own lives and were not gang-raped and murdered.
[NEXT_CONCEPT]
The 66-year-old Fields twins, from Missouri, have lived together all their lives - now they are even closer after sharing their skin.