Pushkar said he approached the police at Civil Lines station on November 27 and lodged the complaint.
Today, he gave a notice to Speaker Ram Niwas Goel demanding a breach of privilege motion against Tyagi, which the former rejected.
"Over-zealous loyalists of AAP thinks whoever questions the party over policies are against them. I have raised certain matters and ended up receiving threats to life inside and outside the House," Pushkar said.
Tyagi rejected the allegations saying he did not know why Pushkar had filed a complaint.
"I sit next to him and we have worked very closely, fought elections together. I realised that he was talking about me in the House. I just asked him what went wrong. I don't understand why is he saying such things," Tyagi said.