As Roy Whiting began a life sentence for abducting and killing 8-year-old Sarah last summer, Home Office Minister Beverley Hughes said that a so-called 'Sarah's Law' would not help to protect children.
Whiting had a previous conviction for the kidnap and sexual assault of a small girl but served just two-and-a-half years of a four year jail sentence, which Ms Hughes said could have been life.
Sara and Michael Payne - Sarah's parents - made an impassioned plea for the right of parents to know if offenders were living near their homes.
But Ms Hughes said: "We're clear that it won't help to protect children.
"It will probably make protecting children even harder for the police for two reasons: it drives offenders to ground, the police don't know where they are, but secondly... it's unworkable - offenders move.
"There's nothing to stop an offender whose name has been disclosed in one area buying a van and driving 100 miles to another area.
'Top priority'
"Parents themselves also move - they visit family as did the Payne family - they go on holiday, so the idea that you can give parents all the time the names of anybody who might be a threat is simply not workable."
Ms Hughes said that it was a "top priority" for the government to legislate to ensure tougher sentencing of violent and dangerous offenders.
Steps had already been taken to extend the period of supervision for offenders who were deemed to pose a risk.
On Wednesday Tony Blair's official spokesman sent his "deepest sympathy" to the parents and family of Sarah Payne.
That came just after Mrs Payne gave her reaction to the guilty verdict on Whiting.
She said: "This doesn't make us happy, but justice has been done. Sarah can rest in peace now.
"Let's make sure that this stops happening time and time again.
"People are being let out of prison when everybody concerned knows that this is going to happen again.
"Why should it be on policemen's shoulders? This is down to the government."
Liberal Democrat home affairs spokesman Norman Baker said it was a "tragedy" Sarah Payne's murder was allowed to happen.
"For the most serious sexual offences, it is quite proper for offenders to be given an indefinite sentence," he said.
A system could be put in place whereby offenders were brought back before a court to assess whether they were fit for release, Mr Baker added.
Sex offenders already face tougher measures implemented since Sarah's death in July 2000.
The Criminal Justices and Court Services Act, which came into force in June 2001, provides for:
A Home Office spokesman said that sentencing for sexual and violent offenders was also under review.