The minister, however, dismissed the claim as "baseless".
Thakur said the minister told him a CBI inquiry would take minimum one year to conclude and that he should trust the state police's investigation.
"At first, I did not understand why the minister said that ... But after his statement in the media that demanding a CBI probe has become a fashion and that he doesn't believe in CBI accusing a Class 11 student, I doubted him ... He wanted to discourage us so that we do not demand a CBI probe," Thakur told PTI.
Singh, the PWD minister in the Manohar Lal Khattar government, said though he visited the Thakurs' house after the boy was killed he never asked them not to demand a CBI probe.
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The minister said that keeping in view the Thakurs' sentiments, he himself spoke to the chief minister and insisted on a CBI probe, which was ordered within a few days.
"It is shocking that baseless allegations are being levelled," he said.
Meanwhile, Thakurs' lawyer Sushil Tekriwal said: "Barun told me that the minister and the father of the accused student are very close to each other."
The minister, however, denied he knew the family of the Class 11 student, who was recently apprehended by the CBI in connection with the killing.
Former Haryana chief minister Bhupinder Singh Hooda said the state government should have handed over the probe to the CBI immediately.
Congress spokesperson Randeep Singh Surjewala said the role of the Khattar government in the case stood "exposed".
"Pradyuman Murder Case - Role of Khattar Govt exposed! As CM Khattar gave clean chits, his minister pressurised the father to not seek CBI probe," he tweeted.
He sought to know why was the state government "scared of a CBI probe?"
"Why was a Cabinet minister trying to scuttle CBI probe? Was it being done with the consent of CM Khattar?" he posted on Twitter.
Sources in the CBI said the crime was committed in just three to four minutes.
The Gurgaon police had arrested a bus conductor, Ashok Kumar, pinning the blame for the crime on him.
In a twist in the case, the CBI recently announced that it had apprehended a senior student of the school in connection with the incident, rejecting the police theory that the killing was the handiwork of Kumar.
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