Mr Straw's announcement comes just days after Sarah's parents held a one-hour meeting with Home Office Minister Paul Boateng.
Instead, Mr Straw has unveiled a package of measures to strengthen the protection of children.
The measures were prompted by public outcry over paedophiles, following the murder of eight-year-old Sarah Payne in Sussex.
Her mother, Sara, has said the campaign for Sarah's Law, similar to American legislation Megan's Law, would continue.
She said she was disappointed, but added: "we knew it would not be easy and we will continue to fight.
"Megan's Law took months of fighting to implement. This is not the end."
Offender rehabilitation groups welcomed the decision, saying it would protect children and prevent child abusers from being driven underground.
Mr Straw said: "I have considered very closely the question whether there could be some form of controlled access to the sex offenders' register.
"But in practice controlling such access would be impossible to enforce.
"To enforce such an arrangement would not, in our judgement, assist the protection of children or public safety.
"The professional agencies are best placed to determine the disclosure of information on sex offenders."
New precautions
The new measures include a statutory duty on police and probation services to assess the risks posed by all sex offenders in the community.
The probation service will also be obliged to ask victims or their families if they want to be consulted about the release of sex offenders sentenced to 12 months or more.
A spokesman from the National Association for the Care and Resettlement of Offenders (Nacro) said the home secretary had resisted calls to change the law in response to an understandable emotional outcry.
He said: "Instead he has made a decision based on what will best protect children.
"Controlled access would rapidly become uncontrolled access because there would be no way of limiting how far the information might be passed on."
He added: "This would drive offenders to ground and undermine, not enhance, the protection of children."
A spokesman for the Association of Chief Probation Officers told BBC News Online: "The package of measures is a realistic and useful step forward.
"The emphasis on putting risk assessment and management on a statutory basis between police and probation service is extremely important."
The News of the World newspaper, which initiated a 'name and shame' anti-paedophile campaign, said it was "disappointed" that the home secretary had ruled out a sex register law.
It added: "Welcome as they are, today's proposals fall short of the changes which we feel are vital."
Public anger over Sarah's death prompted some people to take to the streets, and in some cases, attacks were carried out on the homes of suspected paedophiles.
In Portsmouth, the residents of a housing estate demonstrated nightly to try to push the council into rehousing people they claimed were sex offenders.
Mr Straw's announcement comes just days after Sarah's parents held a one-hour meeting with Home Office Minister Paul Boateng.
Sara and Michael Payne, both 31, had asked for new legislation to allow greater access to the sex offenders' register - a so-called Sarah's Law.
After a meeting with Mr Straw, the Paynes, from Hersham, Surrey, said they had found common ground in some areas, such as tougher sentences, and had disagreed on others.
The proposals include:
Mr Straw said the tragedy of Sarah Payne's death had touched everyone's lives.
"We have, I believe, recognised the very strong public concern which her murder has evoked," he said.
"The intention of these measures is to provide stronger safeguards for children and also to reassure the public about risk management of sex offenders in the community through the provision of more information about these arrangements."