|Police estimate there are 50,000 people who have accessed child abuse images in the UK|
Keith Bristow said expecting all the estimated 50,000 people in the UK who have accessed abuse images to be brought to justice was "not realistic".
He said police would have to focus on those who posed most risk.
Labour called it "disgraceful", adding that the NCA was not fit for dealing with the problem. The Home Office said all crimes should be investigated.
Some 660 arrests were made during a recent operation targeting people who had accessed child abuse images online.
However, the BBC understands that as part of that investigation, as many as 20,000-30,000 individuals were identified as potential offenders.
The Child Exploitation and Online Protection Centre (Ceop) - part of the NCA - has estimated that 50,000 people in the UK are involved in downloading and sharing images of child abuse.
|Keith Bristow said it was time for an "uncomfortable" conversation about tackling abuse|
"But in my judgement, if there are 50,000 people involved, we won't be able to identify all of them and we won't necessarily be able to bring all of them to justice."
He said the agency's priority was to concentrate effort on the "most dangerous people" and those most likely to carry out physical abuse.
But campaigners pointed to a link between accessing abuse images and "contact offending".
A 2012 Ceop report found "compelling evidence" that those who possessed child abuse images should be considered a risk to children.
It's hard to believe that CEOP and NCA don't seem to understand that there is no victimless child porn. That every image or video is a result of child sex abuse. It really has little to do with whether or not a kiddie-porn user is likely to hurt children - he already has!
It is an honest admission, which it would have been easier not to have made.
But it is clear that police forces and child abuse experts are dealing with a flood of potential evidence - partly the result of increasingly sophisticated software which can detect the digital fingerprint of abusive images online.
The implication is that police forces and the NCA will have to review their cases to determine those where immediate action is needed to protect children, those where more time can be taken, and those which will simply have to be left on file.
This brings obvious risks. A suspect who has viewed indecent images online but, to date, done nothing abusive in the "real world" may offend at a later date.
Keith Bristow's comments - at a briefing for specialist reporters - did not include a call for more resources. There is little doubt others will take up those reins.
The NCA said in July that the 660 arrests made as part of Operation Notarise included teachers, medical staff, former police officers, a social services worker and a scout leader.
Some of the suspected paedophiles had terabytes - equivalent to 1,000GB - worth of data on their hard drives or storage devices.
Mr Bristow said every image would be assessed, describing it as "high volume" work that had to be done at pace.
"It's uncomfortable but we're going to work through it in a logical way, target the most risky first."
|The government said the NCA was leading an "unprecedented operation" against child abusers|
An NCA spokesman said that included preventative measures and enabling young people to protect themselves online - such as blocking search terms and disrupting anonymous web browsing.
NCA deputy director general Phil Gormley said: "Not every viewer will go on to be a contact abuser," adding that further research was required. Shaking head!!! Didn't we just have this discussion with John Grisham?
"We need a much more nuanced, much more sustainable approach to this and we need to confront some really unpleasant and horrible truths about human nature." Amen!
The NSPCC said the NCA's intervention revealed "an uncomfortable truth about the difficult decisions officers face daily in identifying and pursuing offenders".
Head of strategy Jon Brown said: "It's true that the police can only do what they can with the budgets available to them.
"The government must make tackling this vile trade a priority in the funding available to the NCA and at a local force level.
"There are clear links between accessing this material and contact offending."
Jim Gamble, who resigned as head of Ceop in 2010, said: "Are we going to say because there's too many we can't do it?"
He added that it was "shameful" Mr Bristow had to "come out and deliver this hard but honest message".
"And the shame belongs with [Home Secretary] Theresa May who has not invested - who has not delivered anything beyond rhetoric to make things better for children where the internet is involved."
Donald Findlater, from child protection charity the Lucy Faithfull Foundation, said police needed to "deploy their resources to go for those who are most directly dangerous to children and are most actively sharing online".
'Unlikely to harm'
He said some among the estimated 50,000 people who had viewed child abuse images would be heavy users of adult pornography.
"Now that's not OK," he told BBC News. "But it does tell me that their primary sexual interest is in adults. They're highly unlikely to directly harm a child." Again, they already have hurt children just by watching child-porn!
Also included in the 50,000 would be younger teenage boys looking at images of girls under 18, he added. Is he suggesting that that is OK?
Labour accused the government of presiding over a policy which saw "the vast majority" of those downloading child abuse images "not investigated".
"Of course they need to look first for the most dangerous cases, but it seems most cases aren't being investigated at all," shadow home secretary Yvette Cooper said.
"Theresa May created the National Crime Agency... but it's clear now that the NCA is simply not fit for dealing with the scale and seriousness of this problem.
|Labour's Yvette Cooper: "This is a disgraceful policy from the NCA and the home secretary"|
Police arrested hundreds of thousands of people for theft and drug offences, she added
But the Home Office said: "We are clear that all crimes should be investigated," adding that the government was "determined to stamp out" what was an "appalling crime".
A spokesman said the NCA had safeguarded or protected more than 1,000 children, making 706 arrests.
"We will always ensure police and other crime fighting agencies have access to the powers and resources they need to tackle child abuse in all its forms," the department said.
Last week Mr Bristow apologised if children had been harmed because of Ceop "sitting on" information it had about 2,000 British paedophiles for more than a year. What? Why? I wondered why there was no flurry of arrests after Operation Spade identified hundreds of pedophiles in the UK.
Information on the men was sent to UK authorities by Toronto Police in July 2012, as part of an international investigation, Operation Spade, into suspected paedophiles.
But it was not passed on to police forces until more than 12 months later in November 2013.
This is incredible! Why?