Thakur, accompanied by his lawyer, told a press conference here that he had appealed to the top leaders of the country to expedite the Central Bureau of Investigation (CBI) inquiry into the "sensitive matter".
Thakur's lawyer alleged that the CBI inquiry had not yet started despite the Haryana government recommending it.
"If the formal inquiry by the CBI is not started by tomorrow, then Barun Thakur will move the Supreme Court on Monday," he added.
The Haryana government has also recommended a CBI probe into the killing of the Class 2 student of Ryan International School.
Pradhuman was found dead in a school toilet with his throat slit. School bus conductor Ashok Kumar was arrested the same day for allegedly killing the child.
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