He says that a man seen in the video and photographs with two women is not him and has asked for an investigation. Mr Kumar pointed out that he is considerably more heavyset than the man on tape.
However sources close to the 36-year-old former minister told NDTV that the video is about six to seven years old, from before Mr Kumar entered public life.
He was a student then, studying law, and likely recorded the video and took the photos himself, the sources said.
Mr Kumar has not been accused of breaking any law. None of the women in the video, nor his wife have complained against him.
But Mr Kejriwal, who AAP says sacked Mr Kumar within 30 minutes of receiving a CD with the video and photos on it, said today, "we will never ever compromise on our core values. We will prefer to die than tolerate wrongdoings."
The Congress's Sharmishta Mukherjee said, "Abhishek Singhvi in a similar tape case had to step down from all party positions, even from parliamentary committees that he was a part of."
Rival parties have called Mr Kejriwal's action against Sandeep Kumar "damage control." The BJP and Congress held protests in Delhi demanding Mr Kejriwal's resignation.
"This is not moral rectitude but a damage control exercise," said former AAP leader Yogendra Yadav, alleging that Mr Kejriwal only acts against people when he can't deny things anymore.
Delhi's Deputy Chief Minister Manish Sisodia has dismissed the allegation of political rivals that Mr Kejriwal knew about the video for over 15 days.