Tim O'Malley now says he believes the men are innocent of killing 13- year-old Carl Bridgewater.
But Mr Howard said on the Today programme, on BBC Radio 4, that he was not going to reopen matters which had already been considered by his predecessor, Kenneth Clarke.
Carl Bridgewater, a paperboy, was shot dead at Yew Tree Farm, Wordsley, Staffordshire, in September 1978, after interrupting a burglary.
Jimmy Robinson, Michael and Vincent Hickey and Pat Molloy, who has since died in prison, were given life sentences in 1979. They and their families have maintained their innocence and there have been growing doubts about the convictions.
Mr O'Malley says there has been a terrible miscarriage of justice.Reuse content