Verma, who apprehends threat to his life and to his family, told a city court that he had no objection in undergoing the polygraph test if he was provided with adequate security and the process was videographed.
Tytler has objected to the test saying CBI has not given any reason for conducting it and its plea for conducting it was "gross misuse of law" and filed with "malafide intention".
Advocate Maninder Singh, who appeared for Verma, said he has been made a witness by the CBI in the case and it would be more proper if the agency records his statement before a magistrate under section 164 CrPC as he would not be able to retract from it.
"If Tytler agrees for the test, I have no objection on it. But if I am going for the test, adequate security should be provided to me and my family, as I am under threat.
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While giving conditional consent, he also said the questions put to Verma during the test should be related to this case only and not to any other case in which he has been made accused by the agency.
The CBI prosecutor, however, said the consent should be unconditional and there should not be any condition.
During the hearing, senior advocate H S Phoolka, who represented riot victims, said keeping in mind the background of the case, the witness should be provided adequate security.
Tytler, who has denied any role in the riots, was given a
clean chit by CBI thrice, but the probe agency was directed by the court to further investigate the matter.
Verma has made several statements to CBI against the senior Congress leader alleging he had pressurised witnesses in the case.
CBI said in its plea that "for the purpose of further investigation, polygraph test (lie detection test) needs to be conducted on Abhishek Verma and Jagdish Tytler". It has cited the court's December 4, 2015 order in which it was mentioned that lie detection test may be conducted, if required.
It had noted that the statement given by Verma to CBI in which he claimed that Tytler had sent the son of Surinder Singh Granthi, a key witness against him, to Canada, cannot be a "sheer coincidence" and the agency should probe whether it was true.
The court had in December 2015 directed CBI to further investigate the matter and said it would monitor the probe every two months so that no aspect is left uninvestigated.