Kejriwal, in a letter to Lieutenant Governor Najeeb Jung, had accused him of trying to "save" Girri and New Delhi Municipal Council (NDMC) vice-chairman Karan Singh Tanwar in Khan's murder.
Girri had asked Kejriwal for a public debate over his allegations.
In a letter to Kejriwal on June 16, Girri had invited him to Constitution Club to produce "evidence" he had against him in the M M Khan murder case on Sunday 4 pm.
The BJP MP has asked Kejriwal to either prove his charge against him or "resign" from the post of Chief Minister.
"If he manages to prove, then I will quit politics, otherwise he should do so," Girri said.
(REOPENS NRG26)
Hitting back at Girri, AAP's Delhi unit convenor Dilip Pandey said an open debate with Kejriwal would not solve the problem, instead the BJP MP should be ready for a fair investigation.
The party also reiterated its demand for arrest of Girri and Tanwar in connection with the murder.
AAP MLA from Okhla Amanatullah questioned Girri's ties with Kakkar.
Pandey also alleged that Tanwar took money from Kakkar to get Khan transferred and the BJP leader had also threatened the NDMC officer.
Pandey claimed that a letter was written by Tanwar to Khan. AAP and people of Delhi want to know the content of the letter which has since gone missing, he claimed.
