Margaret Whitcombe, 41, was shot at point-blank range in the doorway of her mother's home in Abertillery, Gwent.
Police called to the scene found her 11-year-old son, Daniel, cradling her body. A man, said by neighbours to be her boyfriend, Neil Jones, was bleeding from knife wounds to his face. Mr Jones, a 42-year-old local man, was in hospital under police guard last night.
Gwent Police took the unusual step of naming the man they want to question as Philip Manning. He was released from Portland Prison in October after serving half a four-year sentence for attempting to murder his wife, who divorced him while he was in jail.
Mr Manning, was last seen early on Christmas Day near the murder scene.
He had greying hair, worn in a pony tail, and was wearing a black leather jacket, blue jeans and training shoes. He was driving a silver-grey Ford Sierra, registration A710 XDW.
Mr Manning was sighted in Kensington, west London, late on Christmas Day, although he has no known relatives or contacts in the capital.
Detective Superintendent Ian Johnston, of Gwent Police, said: "We consider Mr Manning to be extremely dangerous. We are very anxious to question him. On no account should members of the public approach him. Anyone seeing him should get in touch with police immediately."
It is understood that he worked as a labourer in the Abertillery area after leaving jail.
Police were warned of his release and the information was passed to the family. Supt Johnston said there was no firm evidence that Mr Manning intended to visit his former wife.
Asked whether he thought tighter security should have been considered, Supt Johnston replied: "It would not be possible in view of all the incidents of violence we have."
Alun Michael, Labour's home affairs spokesman, yesterday called for tough new powers to enable the courts to impose restrictions on violent offenders released from jail in order to protect their victims, in the wake of the murder.
But the Home Secretary, Michael Howard, insisted that in cases where an offender had completed his sentence the authorities had no option other than to let him go - even if they had reason to believe he might still pose a threat to his former victim.
Mr Michael said that there was a growing number of "worrying and often frightening" cases involving offenders posing a threat to former victims.
"The fears are often predictable and the court which has heard all the evidence is in a position at the time of sentencing to understand the relationships," he said.
"That is why Labour proposes that at the time of sentence the judge should have the power to require that in appropriate circumstances the victim or the victim's family be kept informed of the arrangements for the offender's release and even specify conditions in rare cases where that is appropriate."
Mrs Manning's murder was a "dreadful case", Mr Howard said, adding: "We must all be very, very moved by what happened."
But he emphasised that neither the Government nor the prison authorities had any power to intervene once offenders had completed their jail sentence.
"If people have completed their sentences then they have to be released. That is the law of the land," he told The World at One programme on Radio 4.
Mr Howard stressed that the sentences were determined by the courts and only in the case of a life sentence could the risk to past victims be taken into account when deciding the release date.
"The important thing is that every effort is made to protect the victims," he said.