Home secretary R K Singh, who was also to appear before the panel, could not attend the meeting.
Kumar informed the panel about the sequence of events of the incident and said the police control room vans reacted "promptly" after receiving the phone call about the crime.
He is learnt to have told the committee that police investigations helped nab the accused within days of the December 16 gangrape.
During the course of the Police Commissioner's deposition, Congress member Sandeep Dikshit, who had recently demanded the resignation of Kumar in the wake of police action against protesters on Sunday, is understood to have said there was a disconnect between officers sitting in rooms and those on the ground.
He said that officials below Station House Officer rank act on their own giving little regard to orders from superiors.
Dikshit is the son of Delhi chief minister Sheila Dikshit who had been demanding that the Delhi Police be brought under the control of the city government. The Delhi Police is under the direct control of the home ministry.