Women's and children's minister Sandeep Kumar was removed from his post by the Delhi chief minister late Wednesday shortly after the "objectionable" tape was sent to him and national television stations.
"We never try to cover up wrongdoings when evidence comes up against our ministers or party workers, unlike other parties," chief minister Arvind Kejriwal said on Thursday.
Kejriwal said on Twitter, announcing the sacking and referring to his anti-corruption Aam Aadmi Party.
Kumar, a married father of one, said he was the victim of a political conspiracy over the tape ostensibly showing him on a bed dressed only in his shorts kissing one of the women.
Only snippets of the video have been aired on news channels but they, along with photographs, appear to also show him kissing another woman.
"This is a conspiracy against me because I was becoming a prominent face of the Dalit community in the city," Kumar told reporters on Thursday, referring to India's lowest social Dalit caste.
"Check the authenticity of the CD. It is a matter of investigation, a conspiracy to suppress me."