The film features a minute-and-a-half "fly-on-the-wall" recording of a conversation between Robert Eades and a psychiatrist about the murder of Sergeant Derek Robertson, stabbed to death after the policeman responded to a 999 call about a sub-post office raid.
The documentary, called Confrontation on E-Wing, was made by an independent producer.
In a statement tonight, the BBC said: "BBC TV executives will be looking at the programme this evening, and we will respond tomorrow." Earlier, a BBC spokeswoman had confirmed it was considering a request to drop the sequence from Derek Lewis, director general of the Prison Service.
The matter was being assessed by the BBC's head of religious broadcasting, the Reverend Ernie Rea.
In a statement, Mr Howard said: "The broadcasting of remarks made by a convicted murderer serves no public interest and is insulting to the memory of Sgt Derek Robertson.
"I entirely share the family's strong objections to the broadcast of the material. I have made my position clear to the BBC and I trust that they will now respond by removing this material from the programme."
Eades stabbed Sgt Robertson - who was armed with only a truncheon - six times. He was sentenced in January to a minimum 25 years' imprisonment.
Earlier in the day MPs from across the political spectrum expressed their disgust at the proposed transmission.
Tory MP Michael Shersby, Parliamentary adviser to the Police Federation, said: "I shall write to the chairman of the BBC and ask him not to transmit the programme.
"It's quite disgraceful that the BBC should transmit a film about this man in custody. That's a totally inappropriate use of television."
The politicians' distaste for the programme, a 50-minute documentary scheduled for screening on Sunday, was mirrored in a statement from the Police Federation's national vice chairman, Ian Westwood.
He said: "We are disgusted that the BBC has spent public money on putting this programme together and are even contemplating transmitting it."
Earlier a BBC spokeswoman said there was "no question of the BBC or the programme condoning serious crime, nor of giving a convicted murderer a platform".
It was intended to examine the pioneering work of psychologists at Long Lartin prison (in Worcestershire) helping criminals to come to terms with the consequences of their crimes.Reuse content