The minister in question, Erasu Pratap Reddy from Kurnool district who holds the Law and Justice portfolio, is related to Janardhana Reddy.
The allegation against Erasu was that he acted as "one of the mediators" between the jailed mining baron and the CBI special court judge Pattabhi Rama Rao in securing bail for Janardhana Reddy in a multi-crore rupee deal.
The AP High Court suspended CBI's first additional special court judge Pattabhi Rama Rao following the investigating agency's exposure of the scandal two days ago.
A criminal case may be lodged against Rama Rao, former judge T V Chalapati Rao and others and stage is set for their arrest.
The CBI is said to have gathered "clinching evidence" against all those involved in the scandal and submitted it to the High Court.
The CBI is going ahead with the investigation of the scandal on the directions of the HC, official sources said.
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Erasu, however, strongly refuted the allegation and offered to quit politics permanently if the charge against him was proved.
The minister, who rushed to Hyderabad from his native district this morning, gave his "explanation" on the issue to Chief Minister N Kiran Kumar Reddy and sought a detailed inquiry.
"I have explained everything to the Chief Minister," he said and maintained that the allegations against him were "totally false".
"I am innocent and have no connection whatsoever with the scandal. Janardhana Reddy may be my relative but I have no links with him.My family has an unblemished political history for decades now, right from the days of my father who served as a Union Minister," Erasu later told newsmen at the Congress Legislature Party office.
He said media reports alleging his involvement in the scandal "pained me and my family immensely" and he would be filing a complaint with the Press Council of India in this regard.
Erasu denied having met Janardhan Reddy in Chanchalguda Jail here. "I visited the jail in my official capacity in connection with some reforms initiatives.I did not meet Janardhana. If I had to meet him, why would I go so openly," the Law Minister asked.
Telugu Desam Party president N Chandrababu Naidu, who was campaigning for the by-elections in Kadapa district, said it was heinous that a minister "played mediator" in the cash-for-bail scandal.
TDP spokesman Varla Ramaiah demanded that the minister either resign from his post or he be dropped from the Cabinet forthwith.