Police are to open a murder inquiry into the Bloody Sunday killings 40 years ago.
The probe has not started because the resources are not available for the four-year investigation, senior officers said.
It follows the Saville Inquiry's report which said civil rights demonstrators shot dead by British soldiers in Londonderry at the height of the Troubles were innocent.
Chief constable Matt Baggott said: "It is a matter that I think we should be investigating and will be investigating."
The Police Service of Northern Ireland has consulted prosecution lawyers as it prepares to open a major investigation. That would require a team of 30 and extra specialist help which are not available at present.
Assistant chief constable Drew Harris said: "This will be and is a long and resource-intensive investigation.
"Sustain it we will, but there are some questions we need to bring to the (Policing) Board in relation to prioritisation of that and other issues in regard to legacy matters."
Thirteen people were shot dead when soldiers opened fire on civil rights marchers in Londonderry on January 30, 1972. Another man died five months later.
A report by Lord Saville unequivocally blamed the Army for one of the most controversial days in Northern Ireland's history.
Key findings included:
:: No warning had been given to any civilians before the soldiers opened fire;
:: None of the soldiers fired in response to attacks by petrol bombers or stone throwers;
:: Some of those killed or injured were clearly fleeing or going to help those injured or dying
:: None of the casualties was posing a threat or doing anything that would justify their shooting;
:: Many of the soldiers lied about their actions;
:: Northern Ireland's Deputy First Minister Martin McGuinness of Sinn Fein was present at the time of the violence and "probably armed with a sub-machine gun" but did not engage in "any activity that provided any of the soldiers with any justification for opening fire".
Mr Baggott today said matters contained in the report should be investigated but asked what the consequences were for keeping people safe now if detectives were diverted from today's crimes.
"I cannot ask the people doing this to take on a whole raft of other tasks which may be serious by themselves," he told the Policing Board in Belfast.
Mr Harris said police needed to strike a balance between protecting life in the present day and the need to investigate historic crimes, so-called legacy issues from Northern Ireland's long conflict.
Controversial killings from the conflict have resulted in 46 inquests being heard, which require police input, an investigation into the death of solicitor Pat Finucane in 1989 and cooperation with the independent Historical Enquiries Team which is looking at all unresolved cases.
Police are presenting a report to the Policing Board on legacy issues in October.
Mr Baggott said the Public Prosecution Service (PPS), which takes court cases, had provided a view on suspected criminal offences during Bloody Sunday and the areas where investigation was warranted. Material in the Saville Report is excluded from criminal proceedings so any investigation would be effectively starting from scratch.
Mr Harris said: "That will be a large investigation obviously and setting aside the resources to properly start that and take that forward is a corporate issue which is under investigation at this time."
He said the probe had not yet begun and police would need to comply with competing parts of the Human Rights Act.
Mr Harris added: "There is not the expertise free and available to undertake an investigation of this size and that is why we are faced with dilemmas around prioritisation.
"The special resources required for this scale of investigation are just not available at this moment to commence an investigation of this scale and length of time. It is an undertaking which will take perhaps three to four years."
Sinn Fein North Belfast Assembly member Gerry Kelly said it was a huge issue for the Bloody Sunday families and he was worried police will not move it forward at the pace that is necessary.
"People have waited a long time for justice in terms of this. The question I want answered is when will we move this ahead, saying they are not ready to move this ahead will be very worrying for everybody," he said.
He criticised a police proposal to send investigators abroad to help with conflicts in the former Yugoslavia while saying they do not have the resources to investigate Bloody Sunday.