Facebook did agree to develop its existing system for reporting abuse
Calls for Facebook to place a "panic button" on its pages have received the support of 44 police chiefs in England, Wales and Scotland, it has emerged.
Police chiefs signed a letter backing the Child Exploitation and Online Protection (Ceop) centre, which wants the link on every page of the website.
Facebook said an existing link allowing users to report abuse will in future enable a report to be made to Ceop.
But Ceop said direct visible access to the button remained "unresolved".
Ceop made public the letter signed by police chiefs - including Scotland Yard Commissioner Sir Paul Stephenson - urging Facebook and other social networking sites to install the Ceop button.
The dispute comes after Peter Chapman, 33, was last month jailed for killing Ashleigh Hall, 17. He made contact with her while using a false identity on the social networking site.
The BBC's home affairs correspondent Danny Shaw said the move suggests the row between Ceop and Facebook is escalating.
He added: "Other independent child protection experts say it's time to call an end to the dispute.
"They say that Facebook is relatively safe, and further damaging publicity could drive users to seek contact in more risky online environments."
Facebook had previously said it would not install a "panic button" on its main pages for users to report suspected paedophiles, but would develop its existing system.
Ceop's director Jim Gamble has had a meeting in Washington DC with Facebook, which says it takes the issue seriously.
Richard Allan, Facebook's head of policy in Europe, said the social networking site and Ceop had a "common agenda" on child safety on the internet.
He said the site had showed Mr Gamble "a series of measures which we think will meet the requirements that he has".
He added: "We're going to build into our reporting structure an ability for people who are in the United Kingdom with relevant reports to go directly to Ceop.
"There are some issues around the design and the way in which we do that that Jim put to us very forcefully but... in order to change a website as fundamentally as he wishes us to do then that takes some time to work through."
Mr Allan said that US-hosted sites such as Facebook already pass reports of abuse onto a similar organisation in the United States, which work with Ceop in the UK.
Facebook currently has a link, through which people can report abuse or concerns about other users to the website.
According to Mr Allan, the site has now agreed to allow another window to pop-up when that link is activated, which will allow those reporting abuse to be able also to make another report to Ceop.
Mr Gamble said he welcomed the fact that Facebook had "committed to improve the way they work with Ceop".
But he added: "However the critical issue remains unresolved. We believe that, without the deterrence provided by direct visible access to the Ceop button on each and every page, children will not be appropriately empowered, parents cannot be reassured and the offender will not be deterred."
Ashleigh Hall, 17, was lured by a man using a false identity on Facebook
The "panic button" in question 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.
Mr Gamble said the issue was an urgent one, especially after the murder of 17-year-old student Ashleigh Hall in County Durham last October by Peter Chapman, a man she met via the site.
Last month Chapman, 33, was jailed for at least 35 years for the killing.
The teenager had been 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".