David Cameron said "it may well be time" to change the law and make failing to report child abuse a criminal offence.
His comment comes after the NSPCC chief executive Peter Wanless said not mentioning abuse in order to save an organisation's reputation should be a crime.
Mr Cameron said at Prime Minister's Questions: "The Government is currently looking at that [changing the law] and of course both reviews will be able to examine this particular point and advise us accordingly. I think it may well be time to take that step forward."
The call by the NSPCC chief to change the law so that failing to report child abuse is a crime has been welcomed by a lawyer who represents 176 victims of disgraced TV presenter and serial abuser Jimmy Savile.
Liz Dux, a lawyer with Slater & Gordon, said: "The NSPCC's backing for mandatory reporting is a welcome and significant moment in our fight to protect future children from predators like Savile, Harris, Smith and Hall.
"This, coupled with an announcement earlier this week by Theresa May that an independent inquiry is to be held, signals we are moving in the right direction - the victims will take some heart.
"Universally the victims I work with say they want change, they support mandatory reporting.
"We must not pass up this opportunity to protect our children and we must not delude ourselves that outrages like these ones will never happen again - if we don't act they could."
The head of the NSPCC, who is leading a review into the Home Office's handling of abuse allegations, said failing to report crimes against children should be an offence.
Not mentioning abuse in order to save an organisation's reputation should be a crime, chief executive Peter Wanless told the BBC.
If someone consciously knows that there is a crime committed against a child, and does nothing about it because they put the reputation of the organisation above the safety of that child, that should be a criminal offence.
Mr Wanless's comments were "hugely welcome" and "a really significant U-turn for the NSPCC", the chief executive of the National Association for People Abused in Childhood, Peter Saunders, said.
The charity had previously said it felt "criminal sanction against those who hesitate is unfair".
A report written by NSPCC, the Royal College of GPs and researchers from the University of Surrey and University College London, states family doctors are ideally placed to spot early warning signs of child abuse.
The report states:
At a time when child protection services are under acute pressure and the role of universal services is under scrutiny, our report raises a crucial question for policy makers and professionals: is it time to rethink the role of the GP for children with maltreatment-related concerns and their families?"
We suggest that reconceptualising the GP's role to include direct responses to certain children and families.
GPs should be given more responsibility to spot cases of child abuse to help prevent the "acute pressure" social services faces in dealing with the problems, a children's charity has said.
The NSPCC claims family doctors are often only seen as a referral service to pass cases along to social services.
However, GPs could do more to help children and families at risk if they were given more autonomy, time and support, they added.
The NSPCC said that GPs could contribute a new "public health approach" that could reduce the number of children needing to enter the child protection system.
The NSPCC has said that there were 8,077 children who were accused of sexual offences - 3,868 in 2012/13 and 4,209 a year later. Crimes included serious sexual assaults, rape and obscene publication offences. NSPCC chief executive Peter Wanless described the results as "deeply concerning".
Most victims knew their alleged abuser, with some of the most common crimes being teenage boys abusing female acquaintances, according to the NSPCC. It said most abusers were male though there was a small proportion of female abusers, and victims were male and female.
"We know that for many older children pornography is now part of life. Easy access to hardcore, degrading and often violent videos on the internet is warping young people's views of what is normal or acceptable behaviour.
Figures obtained by the NSPCC show more than 8,000 under-18s were accused of sexual offences against other children in the last two years.
The children's charity contacted 42 police forces across England and Wales with a Freedom of Information request asking for the number of under-18s who had been accused, the youngest victim and the youngest accused. Of the police forces contacted, four did not respond.
The youngest child to be accused was aged just six, while the youngest victim had not yet reached their first birthday.
Rolf Harris hid behind his "happy-go-lucky persona" while committing a string of sexual offences which damaged the lives of his victims, a children's charity has said.
The NSPCC received 28 calls about the veteran entertainer through its helpline, including 13 people who said they had been abused by him.
Speaking after the guilty verdict, Peter Watt, director of national services at the NSPCC, said:
We’re delighted to have played a major role in helping bring Rolf Harris to justice and to uncover the dark side of an entertainer who hid behind his happy-go-lucky persona while committing sexual offences.
His reckless and brazen sexual offending, sometimes in public places, bizarrely within sight of people he knew, speaks volumes about just how untouchable he thought he was.
Like many children overwhelmed by the trauma of sexual abuse, those he targeted struggled to understand the ordeal they had been through at the time, and battled to come to terms with the impact of their experience at his hands. Some felt ashamed at what had been done to them.
But now the world knows only one person should be ashamed, and that is Rolf Harris.
Parliament must "recognise extreme emotional abuse" and give child protection services greater power by legislating against it, a senior member of the NSPCC said.
John Cameron, head of child protection operations, said the so-called "cinderella law" was not about punishing parents who did not buy their children "the latest gadgets or trainers":
The Government has indicated they are set to outlaw extreme emotional cruelty and this is a positive step forward and the publicity around this and highly publicised cases such as Daniel Pelka may have contributed to the sharp increase in calls.
We must recognise extreme emotional abuse for what it is - a crime - and those who carry it out should be prosecuted.
This isn't about prosecuting parents who don't buy their children the latest gadgets or trainers, this is about parents who consistently deny their children love and affection.
Peter Watt, the NSPCC's director of national services, said:
The responses these victims received when they first revealed Savile's sickening crimes makes heart-rending reading.
They were ignored, dismissed, not believed, laughed at and, astonishingly, told in some cases they should feel lucky he had paid them attention.
Half a century on, the world finally discovered just how dreadful his crimes were - something these men and women had known all that time but felt powerless to do anything about.
The anger, frustration and sheer helplessness of the situation obviously damaged their lives in various ways.
But they showed true courage in coming forward once more to talk about their experiences and hopefully they can now start to put the terrible trauma behind them.