Official sources said he has now been called by the agency on January 16.
The investigating officer (IO) of the case had earlier this month summoned him for appearance today, which he skipped.
The sources said an authorised representative of Karti Chidambaram today met officials probing the case and handed over some documents.
The central probe agency had registered a case against him and others in May this year.
It had registered an Enforcement Case Information Report (ECIR), the ED's equivalent of a police FIR, against the accused named in a CBI complaint, including Karti Chidambaram, INX Media and its directors, Peter and Indrani Mukerjea.
The ECIR was lodged under the provisions of the Prevention of Money Laundering Act (PMLA).
The sources said that the ED will probe the alleged "proceeds of crime" generated in this case.
It was the ED which had provided information about the alleged illegal payments made by INX Media, based on which the Central Bureau of Investigation had filed its FIR.
The CBI had also carried out searches at the homes and offices of Karti Chidambaram across four cities for allegedly receiving money from the media firm owned by the Mukerjeas to scuttle a tax probe.
The CBI had filed the FIR against Karti Chidambaram and the Mukerjeas on charges of criminal conspiracy, cheating, receiving illegal gratification, influencing public servants and criminal misconduct.
The agency has alleged that Karti Chidambaram received money from INX Media for using his influence to manipulate a tax probe against it in a case of violation of Foreign Investment Promotion Board (FIPB) conditions to receive investment from Mauritius.
The CBI has said it has also recovered vouchers of Rs 10 lakh which were allegedly paid for the services.
These vouchers were issued in favour of Advantage Strategic Consulting (P) Limited, a firm "indirectly" owned by Karti Chidambaram, the CBI had alleged.
Former finance minister P Chidambaram, after the CBI searches on May 16, had issued a strong statement in response to the raids, saying the government was using the CBI and other agencies to target his son.
The FIPB approval was granted in "hundreds of cases", the senior Congress leader had said.
The CBI FIR was made out against Karti Chidambaram, his company Chess Management Services, the Mukerjeas (currently in jail on charges of murder of their daughter Sheena Bora), INX Media, Advantage Strategic Consulting Services and its director Padma Vishwanathan.