The accused has been identified as Harsh Sahay Gurjar and was held from Ganganagar in Sawai Madhopur district, Jadeja told reporters.
He said that three-four days after the minor's body was found, the police also recovered the body of a woman from the same area, and that there was a 'high chance' that the woman might be the victim's mother.
It was possible that the accused was behind the killing of both the persons, Jadeja said.
He said a vital lead in the investigation of the crime came when the police, scouring CCTV footage of Pandesara area, where the girl's body was found, zeroed in on a black car.
The minister said the ownership of the car was traced to a stone contractor at whose place the girl and her mother, originally from Rajasthan, were working.
The contractor told the police that his brother had gone to Rajasthan in that car and that he suspected his involvement, Jadeja said.
"Since the accused went in the car to Rajasthan, the contractor told police that he suspected that his brother might be behind the crime," Jadeja said.
The minister said Gurjar even tried to dispose off the girl's body using the black car. "We believe that he has killed both of them. We will be conducting DNA tests to verify if the there is a relationship between the woman and the girl," he said.
He said a special public prosecutor would be appointed for a speedy trial to bring the accused to justice.
The body of the minor girl, possibly 9-11 years of age, was found in the bushes in the Pandesara area on April 6.
The body bore 86 injury marks, including on her private parts, and a doctor at the city civil hospital had said the nature of her injuries suggested she had been held captive, tortured and raped.
The postmortem report stated that she was strangulated to death.
A first information report was lodged under sections 302 (murder), 323 (voluntarily causing hurt), and 376 (rape), and under provisions of the Protection of Children from Sexual Offences (POCSO) Act against unidentified persons, police had said.
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