Chief Constable Hugh Orde has said he never intended to cast doubt on the Bloody Sunday inquiry.
The inquiry is examining the events of Bloody Sunday
Mr Orde earlier said the Saville Inquiry was "a waste of money".
He said society needed to draw a line under its history in an interview with the Financial Times newspaper on Tuesday.
He said the Saville Tribunal was unlikely to satisfy the families or any of the other groups involved.
The chief constable was responding to Sinn Fein demands that the police ombudsman be given powers to investigate all allegations of past misdeeds by officers.
He obviously doesn't understand the relatives' feelings and how much it matters to them in determining the truth
Michael McKinney Victim's brother
The inquiry is examining the events of 30 January 1972 when 13 civilians were shot dead by British Army soldiers during a civil rights march in the city.
A 14th person died later.
Mr Orde was quoted in the paper as saying: "Apart from making lawyers millionaires, will it satisfy the families? I don't think so."
He added the inquiry costs would pay for two police colleges.
However, in a statement released later on Tuesday, Mr Orde said it was important to find out the truth about what happened on Bloody Sunday and "it certainly was not my intention to cast doubts on the legitimacy of that inquiry".
"Society has a responsibility to find out what has happened in historical cases, but we must also meet the needs of the present.
"There are a growing number of calls for investigations into historical cases, and what I was saying is that perhaps now is the time to look again at how we go about establishing the truth and meeting the needs of victims and their families."
SDLP leader Mark Durkan said: "On this issue the chief constable has displayed insensitivity and ignornace that has not marked his contribution up until now.
"His comments are not just hurtful to many, but damaging to himself and should be withdrawn."
The tribunal, is due to resume in London next week, but it will be the middle of next year at the earliest before Lord Saville is due to complete his report.
Search for justice
Last year, Northern Ireland Office minister Des Browne said the total cost of the inquiry could be more than £126m.
Mickey McKinney, 51, whose brother William was one of those killed said: "Once this tribunal begins getting at the truth - and I think it is getting at some of it - the only battering ram the critics have is the costs.
"I'm astonished he should make those remarks.
"He obviously doesn't understand the relatives' feelings and how much it matters to them in determining the truth and our request for a declaration of innocence for all our people."
SDLP policing spokesman Alex Attwood questioned the chief constable's judgement.
"There is a real concern that the tribunal will not expose the truth and that families and others will not be satisfied," he said.
"The truth however must prevail.
"It is important for all leaders in the north, including the chief constable to more fully acknowledge this requirement.
"Failure to do so is hurtful to families and unhelpful to creating a just society."
Sinn Fein chairperson Mitchel McLaughlin described Mr Orde's comments as a "complete red herring".
"The fact is that inquiries need not cost anything and the British Government must face up to the actions of its agents," he said.
Lord Saville of Newdigate and the commonwealth judges accompanying him on the Bloody Sunday inquiry began their work nearly four years ago.
They are not expected to report back until 2004.
The Bloody Sunday inquiry was established in 1998 by Prime Minister Tony Blair after a campaign by families of those killed and injured.
They felt that the Widgery Inquiry, held shortly after the shootings, did not find out the truth about what happened on Bloody Sunday.