The agency, which produced Karti Chidambaram before special judge Sunil Rana after his five-day police custody expired, said an extension was needed as there were "new revelations". Further custodial interrogation was necessary to confront him with "new facts", it added.
Though there was "substantial progress" in the last four days of investigation into the case, he "had not been cooperating" and not disclosing passwords to his phones, it said.
The agency also alleged that witnesses in the case were being approached and evidences destroyed.
The CBI, which had sought nine days of police custody of Karti Chidambaram, said he was taken to Mumbai and confronted with Indrani Mukerjea, one of the then promoters of INX Media, at the Byculla prison and her statement was just one of the evidences.
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"New revelations in the matter have come up day before yesterday. Cannot divulge much about investigation but we need his further custody to confront him with the new facts," Additional Solicitor General (ASG) Tushar Mehta, appearing for the CBI, told the court.
However, the court posted the hearing on the bail plea on March 9 when Karti Chidambaram will be produced before it after his three-day police custody.
During the period of remand, all the conditions laid down in the March 1 order will prevail -- that Karti Chidambaram will be medically examined every 24 hours and will be at liberty to seek the assistance of his counsel , one hour each in the morning and evening.
Senior advocate Abhishek Manu Singhvi, appearing for Karti Chidambaram, said the CBI just wanted to keep him in custody by hook or by crook.
"I have cooperated. I am not obliged to answer what you (CBI) want to hear. My duty is only to make myself available for questioning," Singhvi submitted.
"The shifting of stands/reasons by the CBI to keep me in custody is a mala fide attempt on their part to get my custody," the senior advocate said.
"Is Indrani's statement even an admissible evidence? She is in jail in murder case of her daughter," he asked, adding that Karti Chidambaram was not a terrorist with a bomb that he could not be interrogated without being kept in custody.
The court had allowed him to meet them for 10 minutes.
At the outset, the probe agency submitted before the court documents in a sealed cover related to the probe in the case over the last six days.
On March 1, the court had allowed Karti Chidambaram's custodial interrogation by the CBI for five days, saying there was need to unearth the larger conspiracy in the INX Media case and his presence would serve an important purpose.
While granting police custody, the court on March 1 had come to the conclusion that Karti Chidambaram's presence was needed for important and specific purposes connected with the completion of the investigation in the present case, the CBI said.
The agency also reminded the court about its previous order in which it was stated that Karti Chidambaram's custody remand was necessary to confront him with documents, co-accused and to unearth the larger conspiracy and the role of other accused person involved in the case.
Rao had headed a committee which dealt with the Foreign Investment Promotion Board (FIPB) issue of INX Media before the approval was granted when Chidambaram was Union finance minister.
Karti Chidambaram was arrested on February 28 at Chennai Airport on his return from the United Kingdom, in connection with the FIR lodged on May 15 last year alleging irregularities in FIPB clearance to INX Media for receiving overseas funds worth about Rs 305 crore in 2007 when his father was finance minister.