The option to contact a “trusted friend” has been added to the website’s safety centre.
Facebook said that the system was designed to help people solve online problems “face to face”.
For more serious concerns, Facebook can put users in touch with police or charities that can help them, said Mr Allan.
“In the real world you have a sense of when you need to escalate something to the right organisation.
“If someone is calling you names, it might not be appropriate to go directly to the police,” he said.
Facebook has come under fire in the past for appearing slow to respond to concerns about online safety.
Among Ceop’s concerns was that Facebook’s response centres may have insufficient staff to cope with reports from its 500 million global users.
Facebook has never revealed how many people it employs to handle complaints of bullying or abuse.
Richard Allan defended the current setup: “We are keen to always have the most efficient procedures and best people in place.
“It is not as simple as a ratio of reports to people. When we pick up a pattern of activity, we can create a system to monitor that,” he said.
As well as trusted friend reports, Facebook has also revamped its safety centre, simplifying the language and improving its guides for adults and young people.
The changes were unveiled during a White House anti-bulling conference.
Ahead of the event, President Obama and his wife Michelle recorded a video message, posted on Facebook, saying that bullying is “not something that we have to accept”.
Facebook recently teamed-up with the Samaritans to launch a reporting system for users concerned that their friends may be at risk of committing suicide.