Senior officers have previously said vigilante groups such as Dark Justice or The Hunted One could put child abuse investigations at risk.
Bahram Hosseini appeared at Leeds Crown Court at the start of the month after travelling from his home in West Yorkshire to Newcastle as part on an online trap to hunt out paedophiles.
Chief Constable Simon Bailey, the national lead for child protection at the National Police Chiefs' Council, told the BBC: "(These) vigilante groups are putting the lives of children at risk.
"I'm not going to condone these groups and I would encourage them all to stop, but I recognise that I am not winning that conversation.
"I think (working with vigilantes) is something we're going to have to potentially have to look at, yes, but it comes with some real complexity."
Related story: Perverted school governor who arranged to meet 'teenage boy' in Leeds caught in livestream online sting by vigilante groupFigures obtained by the BBC show an increase in the number of cases where evidence gathered by paedophile hunters is being used.
More than 44% (114 of 259) cases of the crime of meeting a child following sexual grooming used this evidence in 2016, compared to 20 out of 176 cases in 2014 (11.3%).
Tyneside-based duo Dark Justice claim on their website to have helped apprehend 104 sex crime suspects, leading to 50 convictions.
A sting operation by a group known as The Hunted One descended into violence as they ambushed a man who sent sexual messages to a decoy account.
Their target, Mirza Beg, 29, was jailed at Maidstone Crown Court in August for 40 months after he turned up with condoms at the Bluewater Shopping Centre in Greenhithe, near Dartford, Kent, believing he was meeting a 14-year-old girl.
Mr Bailey warned that paedophile hunters' activities could hamper existing police operations.
"I don't encourage or condone the activities of these paedophile hunters, because we only ever hear of the cases where they believe it has gone well," he told BBC Radio 4's Today.
"They don't take into consideration the safeguarding risks to children, the implications of a failed operation or the compromise of one of our own operations.
"So I don't believe that vigilantes are the answer to this problem."