Delhi Congress chief Ajay Maken released a sting video, purportedly showing a man seeking money from one Qaseem. Maken claimed the man was Hammad, a staffer at Hussain's office. The man was also heard saying that they had to "give money" to get an AAP ticket in the assembly polls.
Congress also released two audio clips purportedly containing telephonic conversations of Qaseem with the minister's brother and an engineer of the municipal corporation.
The AAP minister, who represents Ballimaran in the assembly, denied the charge as "baseless".
"I have nothing to do with the sting. The allegations are totally baseless. If Maken can prove the charges, I will quit politics. He should quit politics, if he fails," said Hussain, the Minister for Food and Civil Supplies, and Environment and Forests.
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Hussain was made minister in October last, replacing Asim Ahmed Khan who was sacked by Delhi Chief Minister Arvind Kejriwal for demanding a bribe of Rs 6 lakh from a builder.
He said he would send copies of the video and audio clips to the Chief Minister and CBI.
Maken demanded that the Delhi Minister resign immediately till an independent probe is conducted into the sting operation.
"Our demand is simple, Hussain must resign and there should be a CBI probe into it," he said.
Replying to questions, the Congress leader said if an impartial probe is held, Kejriwal too "cannot remain untouched" as there have been charges of selling tickets during polls.