Mohd Abdul Waheed Chisti, a reporter with a local Urdu daily, raised a question relating to the ownership of the disputed site before the construction of the Babri mosque in Ayodhya.
Chisti asked the Shahi Imam to spell out his stand on the mention of King Dashrath's name in land records of 1528 before the Babri mosque was constructed.
Initially, Bukhari skirted the question but when the journalist insisted, he was threatened.
"Get him out of this conference, Bukhari shouted while accusing the journalist of working against the interests of the Muslims.
Bukhari's supporters then thrashed the journalist in full public glare. People like him will "not be tolerated by Muslims at any cost," the Shahi Imam said before leaving the press conference.
Chisti said he was only seeking a clarification from Bukhari, who had needlessly got provoked.
The journalist later filed an FIR against Bukhari and his supporters at Hazratganj kotwali.
Earlier, Bukhari said the September 30 verdict of the Allahabad High Court on the Ayodhya title suits was based on faith and was not acceptable to the Muslims.
He said there was no question of evolving a consensus or even holding talks for giving the mosque site for temple construction.
The Lucknow bench of the Allahabad High Court had directed that the 2.77-acre disputed site be divided into 3 parts. Of this, 2 parts go to the Hindus and the remaining to the Muslims.
On efforts by Hashim Ansari, the oldest litigant in the title suits, for an out of court settlement, Bukhari said he did not take him seriously as he was "changing his statements frequently."