CC Fahy said other police work was compromised by thousands of calls better dealt with by social workers and such searches cost the force £30m a year.
English, Scottish and Welsh police dealt with 306,000 missing people in 2012/13, according to the latest UK Missing Persons Bureau figures with each missing person call costing an average of £1,325 according to research.
The soon to be retiring chief [full story here] gave his thoughts as part of a debate started by the head of the NPCC, Sara Thornton, who said that the public should no longer expect to see a police officer following crimes such as burglary, and encouraging a "conversation with the public" over priorities.
"We need a different approach," said Sir Peter. "The public and politicians have made it clear that they don't want to see young people being put at risk in these situations because of the concern about what happened in places like Rochdale and Rotherham.
"Every single day, sergeants and inspectors have to make hard decisions about what they are going to do, and missing children will always be top of the priority list. That means there will be other calls that we can't attend to, where we try to deal with them on the phone and where, perhaps appointments get cancelled, where crimes are put off to be investigated on another day."
GMP's response to the problem has been to set up a special team of detectives, dedicated to tracking down and returning missing people.
However, Andrew Christie from the Association of Directors of Children's Services says it's important agencies work together.
"Young people who go missing have usually entered care as teenagers and have very complex needs and behaviours which we are trying to change," he said. "It requires the help of all agencies, including the police, to change these behaviours, and to recover the young people who have gone missing, sometimes several times.
"While we do recognise the additional burdens facing the police service, they do share a legal safeguarding duty and in return it needs to be recognised that our members are facing similar pressures."
The Minister for Preventing Abuse and Exploitation, Karen Bradley, added that they expect all agencies, including the police, to work together to identify and protect missing young people.