However, Bharti, who belongs to Aam Aadmi Party, and Chief Minister Arvind Kejriwal put up a stout defence saying the court was "wrong" in the matter.
The demand for his resignation came in the wake of reports on a ruling by Special CBI judge Poonam Bamba in a case in August, 2013 that the conduct of Pawan Kumar and his advocate (Bharti) "is not only highly objectionable and unethical but also amounts to tampering with evidence."
The CBI Judge had made these observations while cancelling the bail granted earlier to Bharti's client, facing trial in a graft case relating to bank fraud.
The court had taken strong exception to the fact that Bharti and his client Pawan Kumar had telephonically contacted one of the prosecution witnesses to extract his opinion on the matter.
Leader of the Opposition in Delhi Assembly, Harsh Vardhan said, "It has been proved that he was caught tampering with evidence in Patiala House Court.
"Even the judge has observed this. In such a situation, I think the people of Delhi demand Somnath Bharti's resignation and if Delhi Chief Minister Arvind Kejriwal talks about ethics, then he should sack his minister," he said.
Arvinder Singh Lovely, President of state unit of Congress which gives outside support to AAP government, said law protector has become a law breaker. A party that came to power on the basis of morality should question its own conscience.
"Are you such a big man that when there is a sting operation against you, then it is incorrect. If a court gives any verdict, then you raise question over that verdict. What you do is right and what others do is wrong
"They should ask their conscience if they have one, what they are doing is just or not...Today the people of Delhi want to know whether is this ethical," said Lovely.
At a press conference, Bharti claimed he was not indicted by the court. He even faulted the court saying it was erroneous on the part of the judge to say "conversation" with prosecution witness amounts to tampering of proof.
"What is prohibited is intimidation. Conversation is not prohibited," he said.
Kejriwal said they want the media to show the recording to the nation.
"You decide what evidence has been tampered with after watching the recording. We respect the court but in this matter the court is wrong...The judge called the sting operation as tampering of evidence. This is not tampering of evidence," Kejriwal said.
Information and Broadcasting Minister Manish Tewari said that the AAP had claimed to have set high standards of public morality and the nation was watching whether they would walk the talk.