The PSNI has suggested that budget cuts mean it will not be policing the past at current levels when its funding drops.
Deputy Chief Constable Alistair Finlay said: "In times of ever decreasing budgets we must focus on policing the threats to society today."
Areas where cuts will be made will be thrashed out with the Policing Board, but he said the PSNI will "make every effort to prevent cuts to front line service delivery".
It follows a warning from Justice Minister David Ford that his department is facing a budget shortfall of at least £47m, once further cuts are brought in in October.
One body that could be at risk is the Historical Enquiries Team – set up in 2005 to investigate the 3,269 unsolved murders committed during the Troubles.
Victims campaigner Alan McBride, who lost his wife in the Shankill bomb, said the past needed to be dealt with.
"Unfortunately, that is going to cost money," he said. "We do need a process that looks at the past and that needs funding.
"Some people say we need to forget about the past, but for people who lost people in the conflict, it's not that easy – and that's a significant number of people for a place the size of Northern Ireland."
Meanwhile, the Police Federation has called on the Executive to rethink the cuts.
Chairman Terry Spence blasted them as "Draconian".
"Policing cannot shoulder a cutback of this magnitude," he said. "We're already under-staffed with a shortfall of some 1,000 officers.
"That situation can only deteriorate further if the PSNI is told to implement these Draconian cutbacks."
Mr Spence said the PSNI was currently losing 20 officers each month, yet recruitment was not matching the loss.
"The net effect will be even fewer officers to maintain public safety," he said,
"This will pose serious question marks over the ability to police major public order situations. It will have a hugely damaging effect on frontline policing and lead to reduced effectiveness in combating crime. Officers are already badly stretched in the performance of their duties. With staff numbers falling, and recruitment not keeping pace with the numbers who are leaving, it's inevitable that an unfair burden will fall on our rank-and-file.
"That situation would be intolerable."
Mr Spence said he plans to ask for meetings with ministers to plead the PSNI's case.
"I would ask Executive ministers to reconsider as there is still time to avert what is bound to become a crisis," he added.
"This is something that can be fixed, and I would urge them to act to protect the police budget."