The party said the Lok Sabha member from Sangrur was only trying to "show" the procedure of asking questions during the Zero Hour.
"Bhagwant Mann was only trying to show to the people how only 20 names were picked from a draw to ask questions (during the Zero Hour).Since representatives from all areas of the country have the right to ask questions in Parliament, this lucky draw system leaves many MPs without a chance to put forth their questions," AAP leader Ashutosh said.
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"Parliament cannot be run by just lucky draw.BJP is trying to deflect attention from the issue of attacks on Dalits in Gujarat," he said.
Senior AAP leader Sanjay Singh also criticised BJP for targeting Mann.
"Adityanath, Sakshi Maharaj, Giriraj Singh are the biggest threat to country's security and these leaders will add glory to Parliament, while Bhagwant Mann will be booked under NSA? What justice is this?(sic)" Singh tweeted.
However, party sources said the controversy could have been avoided.
"It was an innocuous video and it was certainly avoidable. He has been told to be careful in future," a source said, adding the party is of the view that the video "doesn't compromise" the security of Parliament.
In the nearly 12-minute video that he shared live on Facebook, Mann filmed his vehicle crossing security barricades and him entering Parliament yesterday.
The MP today appeared before Lok Sabha Speaker Sumitra Mahajan and tendered an "unconditional apology" for making the controversial video, which caused an uproar in both the Houses of Parliament.
Terming Parliament as the highest temple of democracy, he said his intent was not to "dishnour it".
"I have not played with anything (security). I have never and it has never been my intent to compromise the security of Parliament. For asking questions during the Zero Hour, there is a lucky draw and only 20 questions are selected.
"People in our constituencies have elected us and sometimes they ask us why we do not raise the issue in Parliament. So, I only wanted to show people the procedure, it was like an educational thing," he said.