The party has been using the site to try to win over floating voters in the run-up to the general election. However, it is now considering withdrawing ads from the network.
Facebook has so far refused to provide a panic button on users' profiles that would allow children to contact police instantly if they think they are being targeted by paedophiles.
It is willing to display a button on its safety and help pages, but has stopped short of introducing a graphic "panic button" widely on its site. It has offered child-protection bodies, including the NSPCC, up to one billion free ad slots on its site, which has 23 million British users.
The Conservative Party's fan page has 23,800 members – the Labour Party and the Liberal Democrats have 7000 each.
A Green Party representative said that although it would like to see the addition of a panic button, it will continue to use the site for its campaigns.
Brands including British Airways and T-Mobile have backed Facebook's position, saying that they will still advertise on the site.