The ED had sought 14 days of custodial remand of Puri.
Special Judge Sanjay Garg also directed that Puri be given proper medical attention during his remand.
"14 days custody remand of the accused has been sought by the ED in order to unearth the larger conspiracy, find out the money trail of proceeds of crime, find out the involvement of other unknown accused persons and confront the accused with documents. Considering the overall facts and circumstances, six days custody remand of the accused is granted," the court said.
ED, which arrested Puri on Tuesday morning in another bank loan fraud case, sought his 14-day custodial interrogation.
The agency had on Monday told the court that Puri was evading probe in the case.
The Delhi High Court today, dismissed the anticipatory bail plea Puri, saying his custodial interrogation was "required for an effective investigation".
Justice Sunil Gaur said that Puri was evasive in his replies during questioning by the probe agency, ED, and it was evident from witness statements provided to the court that he was trying to influence them.
"This court is of the prima facie opinion that custodial interrogation of petitioner (Puri) is required for an effective investigation... Upon considering this case in entirety, this court finds that grant of pre- arrest bail to the petitioner would stall the effective investigation in the case," the court said.
It also said that mere attachment of his property in income tax proceedings would not justify grant of pre-arrest bail to him.
The order came after the court earlier on Tuesday heard arguments on behalf of Puri and the Enforcement Directorate (ED), which opposed the anticipatory bail plea.
Additional Solicitor General Aman Lekhi, representing ED, said Puri was evasive in his replies to the agency during investigations and his answers were ex-facie misleading.
Senior advocate Abhishek Manu Singhvi, appearing for Puri, argued that he was cooperating in the investigation and legal malice and vendetta was writ large in the agency's conduct.
Puri, in his plea through advocate Vijay Aggarwal, had challenged the August 6 order of the trial court dismissing his anticipatory bail plea.
On August 9, the trial court issued a non bailable warrant against Puri on ED's plea.