The site was criticised for not having "panic buttons" on every page, and its director Jim Gamble has said the matter was urgent especially after the murder of a teenager by a man she met on the site.
Speaking after the four-hour meeting, Gamble said Facebook was "one small step from doing the right thing" but had not agreed to his demands outright.
"What I am pleased about is there is a commitment from them to improve what they provide to UK policing," the BBC quoted him as saying.
"There is no doubt they are looking to improve their position around child safety and we recognise that. What I am looking for is turning words into action.
"In our view they are experts at creating a fantastic online environment but they are not experts in law enforcement, the power of deterrents and the reassurance it brings for mums and dads," he stated.
Chief constables from across England and Wales, including Scotland Yard Commissioner Sir Paul Stephenson, have signed a letter supporting the addition of the extra safety feature.
Facebook has said it takes the issue seriously and welcomed the meeting, though it 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.
The company said it would install links to organisations including Ceop on its reporting pages but Gamble said he could not understand why Facebook would not agree to adopt the button on every page as it was a free way to "help save some children".
"If you're going to operate a business that encourages people to frequent your public place so that you can advertise to them, then let's look after them while they're there," he added.