Ashleigh Hall, 17, was lured by a man using a false identity on Facebook
Facebook says it will not install a "panic button" on its main pages for users to report suspected paedophiles, but will develop its existing system.
The company says it will have links to organisations including the Child Exploitation and Online Protection (Ceop) centre on its reporting pages.
But the director of Ceop says there should be a button on every page.
The conviction of Peter Chapman for the murder of 17-year-old Ashleigh Hall led to renewed calls for a "panic button".
The convicted sex offender lured the teenager to her death using Facebook.
Earlier, the Home Secretary said Facebook executives had told him they had "no objection in principle" to installing the safety button.
Alan Johnson said he and the site's executives had had a "frank exchange of views" during the meeting, following calls for Facebook to link to the Child Exploitation and Online Protection (Ceop) centre.
But Richard Allan, director of policy for Facebook Europe, made clear the company was not considering including the button on its main site.
He said the Ceop button might be effective in principle, but only "for other sites", and not Facebook.
Jim Gamble, head of Ceop, said the button needed to be on the front page of every Facebook profile page.
"So that children are reassured and empowered, so are their parents, and offenders are deterred. That's the key.
By Mark Ward, Technology reporter, BBC News
The "panic button" that Facebook is being asked to adopt is already used by other websites, including Bebo. Clicking on it takes people to a site that details how to handle cyberbullying, hacking, viruses, distressing material and inappropriate sexual behaviour.
By putting the button on sites, the Child Exploitation and Online Protection Centre (Ceop) hopes to make it easy for children to find and get help. Ceop says that currently children make about 500 reports a month by clicking on the button. Of those, four a day are from a child in immediate danger, it claims.
Facebook is under pressure to adopt the button because it is a huge source of problems, according to Ceop. Ceop estimates that in January about 75% of reports it received were about incidents on Facebook.
"Facebook is a great environment, they are experts on advertising and engaging with young people in those areas where you can get click-through. But they're not experts on child protection."
Emma-Jane Cross, head of Beatbullying, welcomed Facebook's proposed change to its reporting function, saying it was crucial people who felt they had been bullied online could get help quickly.
"That's why Beatbullying is pleased that Facebook are taking the right steps by working with third sector organisations like us and referring their users to a safe environment where they can get the correct support and advice they need," she said.
Speaking about the meeting, Mr Johnson said: "I emphasised that including the Ceop abuse reporting button on their site has the potential to transform child protection - and that the company should put this above all other considerations."
He said a high-level meeting would be held between Facebook and Ceop officials in Washington on 12 April to discuss it further.
Facebook 'deeply saddened'
Defending Facebook's current set-up, a spokesman said they had been pleased to provide Mr Johnson with further details about their "robust reporting system".
"This innovative system has been developed by analysing millions of reports submitted over the years and testing ways to continually improve our system.
"The system effectively handles all manner of potential abuse we see on the site, ranging from the common minor breaking of the rules, such as embarrassing pictures, to the extremely rare serious matters that are quickly escalated to law enforcement."
He said they had gone on to explain that the website was "exploring ways to improve safety", which included adding links to more organisations, including Ceop and Beatbullying, on Facebook's reporting pages.
"We will also explore adding the Ceop button to our safety centre," he added.
Peter Chapman, 33, was jailed for at least 35 years this month for killing Ashleigh Hall last October.
She was raped, suffocated and her body dumped in a field near Sedgefield, County Durham, after agreeing to meet Chapman.
Earlier that month, she had been attracted by a picture of a young, bare-chested man that Chapman - calling himself Peter Cartwright - had posted on Facebook.
Facebook said it was "deeply saddened by the tragic death".