The boss of Britain's second-largest police force has admitted more than half of the crimes in his area are not investigated.
Great Manchester chief constable Sir Peter Fahy said officers had to concentrate on the most serious crimes and preventing offences.
His comments come with forces across the country facing swingeing cuts of 20% to their budgets.
Fahy, who is vice-president of the Association of Chief Police Officers, said his officers are only able to concentrate on around 40% of reported crime.
He said: "Most crime is committed by a group of active, persistent offenders who go in and out of the criminal justice system.
"So, in continuing to reduce crime, we balance between investigating offences after they have happened and targeting
those who we know are out there every day, looking for criminal opportunities.
"Some of these we visit twice a day to keep them on their toes.
"In the same way that the health service concentrates on the most serious illnesses and the treatments likely to have most effect, the police have to concentrate on the most serious crimes and those where there are lines of investigation likely to produce evidence of the offender.
"In practice, this translates into about 40% of crime being actively pursued at any time. We look at all crimes to identify patterns of offending and to build the picture of where we need to target police patrols. In many crimes there are no witnesses, no CCTV and no forensic opportunities."
Greater Manchester Police needs to save £145.5 million over the four years of the spending review until March 2015, with a report by Her Majesty's Inspectorate of Constabulary (HMIC) this summer stating how the force had planned to cut police officer numbers by 19% over the five years to that deadline.
Tony Lloyd, GMP police and crime commissioner, said: "Let me be clear that I expect, and the chief constable expects, that with all serious crime no effort will be spared to bring the criminals to justice.
"With the most persistent group of regular criminals, local police must and do keep pressure on them to deter them from committing more crime.
"What I don't expect is where there are no witnesses or no evidential trail that the police go through a paper chase to simply tick boxes, but instead use intelligent policing to prevent a recurrence of those types of crime.
"The public should know that when they report a crime and there are reliable witnesses and reliable leads, that it will be investigated.
Blackley and Broughton Labour MP Graham Stringer said the public expect officers to investigate criminal behaviour.
He told the Manchester Evening News: "That sounds like bureaucratic gobbledegook. De-prioritising the majority of crime is bound to lead to a loss of confidence in the police force.
"I think those victims (whose crimes aren't investigated) have every right to be angry."