Justice S P Garg told the CBI to file a status report before March 16.
The CBI, however, contended that the matter was not maintainable.
During the hearing, senior advocate Kapil Sibal, appearing for Karti Chidambaram, informed the high court that he would withdraw the bail plea from the trial court.
Earlier in the day, the matter was posted before Justice Indermeet Kaur who recused herself from the case and said she would refer the matter to the Acting Chief Justice for assigning the bail plea to another bench for today itself.
The bail plea was yesterday mentioned before a bench of Acting Chief Justice Gita Mittal and Justice C Hari Shankar and listed for hearing today.
Karti Chidambaram, the son of former Union minister P Chidambaram, had moved the high court seeking bail, hours after a court here sent him to judicial custody till March 24.
Karti's parents P Chidambaram and Nalini Chidambaram, both senior advocates, were present in the courtroom.
The court had also dismissed his appeal for an urgent hearing on his bail plea and the "threat perception" due to the fact that his father, as a Union minister in the previous UPA government, had handled several sensitive issues.
The court had sent him to Tihar Jail after the CBI, in whose custody he was quizzed for 12 days in a row after his arrest on February 28 from Chennai, said he was no longer required for further custodial interrogation.
The court said his bail plea would be heard on March 15 as scheduled.
Karti was arrested by the CBI on his return from the United Kingdom in connection with an FIR lodged on May 15 last year. It alleged irregularities in a Foreign Investment Promotion Board (FIPB) clearance given to a media house, INX Media, for receiving funds of about Rs 305 crore from overseas in 2007 when his father was the Union finance minister.
The CBI had initially alleged that Karti Chidambaram received Rs 10 lakh as a bribe for facilitating the FIPB clearance to INX Media. It, however, later revised the figure to USD 1 million (about Rs 6.50 crore at the current exchange rate and Rs 4.50 crore in 2007).
The fresh evidence in the case, which triggered Karti's arrest, was based on a statement of Indrani Mukerjea, former director of INX Media (P) Ltd, who recorded it under Section 164 of the CrPC before a magistrate on February 17.