Earlier, he was asked to submit his explanation to the committee by Tuesday morning.
"Since Mann had sought three more days, we have now asked him to respond by July 28. We have to hear his side before arriving at a conclusion," said a member.
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The committee would ask them to explain the security aspects of the complex and areas surrounding the building.
The committee, which has decided to meet every day, will also hear others "associated" with the incident. These could include other MP and security staff, who could have seen Mann videographing the complex.
In the nearly 12-minute video, apparently shot on July 21, Mann gives a running commentary as his vehicle crosses security barricades and enters Parliament. "I'll today show you something you would not have seen earlier," he says.
Mann then enters a room where questions to be taken up inside Parliament are being sorted and describes the process.
Acting tough, Lok Sabha Speaker Sumitra Mahajan on Monday said Mann's videography of the complex had put its security "in peril" and asked him not to attend the House till a decision is taken on the matter.
AAP's arch rival in Punjab, the SAD, has no member on the panel investigating the issue.